Epeunhtikì antikeðmeno: Sunarthsiak Anˆlush-Majhmatik OikonomÐa.

Transcription

1 BIOGRAFIKA STOIQEIA Onomatep numo: Iwˆnnhc Polurˆkhc Jèsh: Kajhght c EMP, Sqol Efarmosmènwn Majhmatik n kai Fusik n Episthm n, mèloc thc Editorial Board tou periodikoô POSITIVITY. Epeunhtikì antikeðmeno: Sunarthsiak Anˆlush-Majhmatik OikonomÐa. DieÔjunsh: Tomèac Majhmatik n, PoluteqneioÔpolh Zwgrˆfou, , Aj na. Thl , ypoly@math.ntua.gr. SUNERGASIES To diˆsthma autì èqw energ episthmonik sunergasða me tic ereunhtikèc omˆdec: (1) Thn omˆda anˆlushc tou PanepisthmÐou thc Alberta tou Kanadˆ pou dieujônetai apì ton Kajhght Vladimir Troitsky, se probl mata diatetagmènwn q rwn kai efarmogèc. (2) Thn omˆda Oikonomik n Majhmatik n (A. Basile- G. Gratsiano) tou University of Napoli Federico II. DIOIKHTIKH EMPEIRIA Febrouˆrioc AÔgoustoc 2001: Dieujunt c tou Tomèa Majhmatik n EMP. DIDAKTIKO ERGO (I) Proptuqiakˆ Maj mata Apì to 1984 mèqri s mera edðdaxa sto EMP ta maj mata: Grammik Algebra, Sunart seic miˆc Metablht c, Sunart seic poll n Metablht n, Midadikèc Sunart seic, Diaforikèc Exis seic, Diaforikèc Exis seic me Merikèc Parag gouc, Diaforik GewmetrÐa. Sta plaðsia tou emploutismoô tou progrˆmmatoc spoud n tou SEMFE me nèec kateujônseic diamìrfwsa kai didˆskw apì to Panepisthmiakì ètoc sth SEMFE ta maj mata Majhmatikˆ Oikonomikˆ (Majhmatik Mikrooikonomik JewrÐa-Eisagwg sth JewrÐa Genik c IsorropÐac) kai Majhmatik Qrhmatooikonomik JewrÐa. Sto Majhmatikì Tm ma tou PanepisthmÐou tou AigaÐou katˆ ta panepisthmiakˆ èth kai edðdaxa ta maj mata Dianusmatik Anˆlush kai Pargmatik Anˆlush. (II) Metaptuqiakˆ Maj mata Sto Metaptuqiakì Prìgramma Efarmosmènwn Majhmatik n tou Tomèa Majhmatik n tou EMP didˆskw suneq c apì to to Panepisthmiakì ètoc : 'Eqei didˆxei ta maj mata: Diatetagmènoi q roi, Majhmatikˆ Oikonomikˆ, Arqèc Qrhmatooikonomik c JewrÐac, JewrÐa mètrou, Sunarthsiak Anˆlush. SUGGRAFIKO ERGO 'Eqw suggrˆyei ta parakˆtw BiblÐa: 1

2 (1) Sun jeic Diaforikèc Exis seic (Pr th èkdosh 1989). Perièqei th basik Ôlh twn Diaforik n Exis sewn. (2) Diaforik GewmetrÐa (Pr th èkdosh 1998). Perièqei th klassik Ôlh thc Diaforik c GewmetrÐac ston R 3. (3) Jèmata anˆlushc kai JewrÐa Genik c IsorropÐac sthn OikonomÐa (2010). (4) Eisagwg sth Majhmatik QrhmatoikonomÐa (EMP, Shmei seic, 2008). EPIBLEYH DIPLWMATIKWN ERGASIWN 'Eqw epiblèyei pˆnw apì 50 diplwmatikèc ergasðec apo tic opoðec oi 17 eðnai metaptuqiakèc diplwmatikèc ergasðec EPIBLEYH DIDAKTORIKWN DIATRIBWN 1. FoÐboc Xanjìc: Olokl rwse th didaktorik tou diatrib metðtlo Diatetagmènoi Q roi kai Efarmogèc sth Majhmatik QrhmatooikonomÐa ton Mˆðo tou Qr stoc Kountzˆkhc: Olokl rwse th didaktorik tou diatrib metðtlo E- farmogèc twn Diatetagmènwn Grammik n Q rwn sth Majhmatik OikonomÐa ton Septèmbrio tou BasÐlhc KatsÐkhc: Olokl rwse th didaktorik tou diatrib metðtlo Jetikèc bˆseic se diatetagmènouc upoq rouc me th Riesz decomposition property ton Ianouˆrio tou ORGANWSH DIEJNWN SUNEDRIWN Up rxa o Organwt c tou diejnoôc sunedrðou Ordered Spaces and Applications (in Economics), EMP, Noèmbrioc Up rxa o Basikìc organwt c tou diejnoôc sunedrðou Eleventh European Workshop of General Equilibrium Theory, EMP, Mˆðoc Up rxa mèloc thc organwtik c epitrop c twn diejn n sunedrðwn: (1) Positivity 30 IounÐou- 4 IoulÐou 2003 Rìdoc. (2) Current trends in economics, Rìdoc, IoÔlioc 1999, Kefalloniˆ Mˆðoc 1995 kai Mˆðoc EREUNHTIKA PROGRAMMATA Sta parakˆtw ereunhtikˆ progrˆmmata up rxa episthmonikìc upeôjunoc (2) Diatetagmènoi Q roi kai Efarmogèc sth Majhmatik QrhmatooikonomÐa (Prìgramma HRAKLEITOS II tou UpourgeÐou PaideÐac). To prìgramma oloklhr jhke me th didaktorik diatrib tou FoÐbou XanjoÔ ton Mˆðo tou (1) Diatetagmènoi Q roi me th Riesz Decomposition Property (Prìgramma K. Karajeodwr c basik c èreunac tou EMP). (2) Efarmogèc twn Diatetagmènwn Grammik n Q rwn sth Majhmatik OikonomÐa (Prìgramma HRAKLEITOS tou UpourgeÐou PaideÐac). To prìgramma oloklhr jhke ton Septèmbrio tou 2006 me mia didaktorik diatrib tou Qr stou Kountzˆkh. 2

3 (3) Efarmog thc Majhmatik c Anˆlushc se Oikonomikˆ Probl mata. (Prìgramma PENED 95). Sto prìgramma autì summeteðqe Ellhnac Epist - monac tou ExwterikoÔ (Q. Aliprˆnthc) kai mèlh DEP apì to EMP, to Oikonomikì Panepist mio Ajhn n kai to Panepist mio Peiraiˆ. (2) NATO International Research Grant (Episthmonikìc upeôjunoc: Q. Aliprˆnthc) (5) Prìgramma Ereunhtik c SunergasÐac me Balkanikèc Q rec (RoumanÐa, 1994) To prìgramma autì qrhmatodot jhke apì to EMP. SUMMETOQH SE SUNEDRIA Eqw pˆrei mèroc sta parakˆtw sunèdria: 1. 13th SAET Conference on Current Trents in Economics, July 22-27, 2013 Paris, France. Orgˆnwse, apì koinoô me ton Kajhght Achille Basile th sunedrðash (Session): Mathematical Economics III kai èdwsa omilða me tðtlo Reflexive Cones (A New Kind of Cones) and Applications 2. Positivity VII, July 22-26, 2013 Leiden, Holland. (Proskeklhmènoc Omilht c 'Edwse omilða me tðtlo Some topics on the theory of cones 3. CSEF: IV Workshop on Equilibrium Analysis, January University of Napoli Federico II, Italy (Proskeklhmènoc Omilht c) 'Edwse omilða me tðtlo Risk measures in Banach spaces economic models and price bubbles 4. ASSET 2012, November 1-3, Limassol, Cyprus ParousÐase ergasða me tðtlo Risk measures in Banach spaces economic models and price bubbles 5. 10th SAET Conference on Current Trents in Economics, June 25 - July 1, 2011 Faro, Portugal ParousÐase ergasða me tðtlo Risk measures in Infinite Dimensional Economies and Bubbles 6. Saint Petersburg, 5-11 Sept ParousÐase ergasða me tðtlo Cones and geometry of Banach spaces o Panell nio Sunèdrio Majhmatik c Anˆlushc, Maðou 2010, Majhmatikì Tm ma tou PanepisthmÐou IwannÐnwn: ParousÐasa ergasða me tðtlo "Mètra kindônou se apeirodiˆstatec oikonomðec ". 8. 8th Conference on Research on Economic Theory and Econometrics T noc IoÔlioc ParousÐase ergasða me tðtlo Maximal replicated Submarkets 9. 9th SAET Conference on Current Trents in Economics, June 29 - July 5, 2009 Ischia, Italy ParousÐase ergasða me tðtlo Maximal replicated Submarkets 10. International symposium on positivity and its applications in sciences and economics, Bolu, Turkey, Sept ParousÐase ergasða me tðtlo Sublattices and financial derivatives 11. Second General Equilibrium Workshop In Rio Jan , 2008, Rio, Brasil. ParousÐase ergasða me tðtlo Demand functions and infinite dimensional e- conomies. 12. Positivity V IoulÐou 2007, Belfast ParousÐase ergasða me tðtlo A cones and a characterization of reflexivity. 3

4 13. XII Conference on Real Analysis and Measure Theory, Ischia,Italy, IoÔlioc ParousÐase ergasða me tðtlo Demand functions and reflexivity. 14. CARTHAPOS 06 A workshop/conference on Positivity, TÔnida, TunhsÐa, IoÔnioc ( WriaÐa omilða) Ordered Spaces and Mathematical Economics th European Workshop on General Equilibrium Theory, Lisbon, Portugal, Mˆðoc ParousÐase ergasða me tðtlo Demand functions and a characterization of reflexivity. 16. Conference on Current Trents in Economics, Vigo, Spain, 27 IoulÐou-3 IounÐou 2005, ParousÐase ergasða me tðtlo Demand functions and a characterization of reflexivity. 17. Positivity IV IoulÐou 2005, Dresden, Germany. ( WriaÐa omilða) ParousÐase ergasða me tðtlo Positive bases in ordered subspaces. 18. XI Conference on Real Analysis and Measure Theory, Ischia,Italy, IoÔlioc Sto sunèdrio autì parousðase ergasða me tðtlo: Eddability of L 1 (µ) in dual spaces th European Workshop on General Equilibrium Theory Iounioc 2004, BenetÐa, ItalÐa. ParousÐase ergasða me tðtlo The Financial Completion in Security Markets (apì koinoô me ton upoy fio didˆktora Qr sto Kountzˆkh). 20. Conference on Current Trents in Economics, Rìdoc 1-7 IoulÐou, 2003, ParousÐase ergasða me tðtlo Pareto Efficient points. (apì koinoô me ton upoy fio didˆktora Qr sto Kountzˆkh). 21. Positivity 30 IounÐou- 4 IoulÐou, Rìdoc. ParousÐase ergasða me tðtlo Empeddability of L 1 in dual spaces and geometry of cones th European Workshop on General Equilibrium Theory 30 Maðou - 1 IounÐou 2003, Bielefeld, GermanÐa. ParousÐase ergasða me tðtlo Existence of Pareto Efficient points (apì koinoô me ton upoy fio didˆktora Qr sto Kountzˆkh). 23. Enato Panell nio Sunèdrio Anˆlushc, Qaniˆ Sept Sto sunèdrio auto parousðase ergasða me tðtlo: Linear Optimization and Portfolio Insurance. 24. X Conference on Real Analysis and Measure Theory, Ischia, Italy, IoÔlioc Sto sunèdrio autì parousðase ergasða me tðtlo: Eddability of L 1 (µ) in dual spaces. 25. International Conference on Functional Analysis and its Applications,(dedicated to Stefan Banach) Lviv, Ucrain, Maðou Sto sunèdrio autì parousðase ergasða me tðtlo: Cones and geometry of Banach spaces. ( WriaÐa omilða). 26. Eleventh European Workshop on General Equilibrium Theory Mˆðoc 2002 EM- P. Sto sunèdrio autì parousðase ergasða me tðtlo: Minimum cost portfolio insurance th Colloquium on Topological Ordered Linear Spaces, Bucharest, Romania, SeptembrÐou Sto sunèdrio autì parousðase ergasða me tðtlo: Geometry of Cones and theory of Banach Spaces. 28. Positivity, Nijmengen, the Nederlands, 9-13 IoulÐou Sto sunèdrio autì parousðase ergasða me tðtlo: The Sructure of Lattice-Subspaces. 29. V Conference of the Society for the Advancement of Economic Theory, Ischia, Italy 2-8 IoulÐou Sto sunèdrio autì parousðase ergasða me tðtlo: Minimum cost insurance and asset pricing. 4

5 30. Ogdoo Panell nio Sunèdrio Anˆlushc (Xˆnjh, Okt brioc 2000). Sto sunèdrio autì parousðase apì koinoô me ton metaptuqiakì Foitht Q. Kountzˆkh ergasða me tðtlo: An ordering in the finite stochastic model of financial markets. 31. Conference on Real Analysis and Measure Theory, Triest, Italy, Septèmbrioc Sto sunèdrio autì parousðase ergasða me tðtlo: Lattice-Subspaces and Positive Bases. 32. Mathematical Analysis and its applications, EMP AÔgoustoc Sto sunèdrio autì parousðasa ergasða me tðtlo: Security Markets. 33. Current trends in economics, Rìdoc IoÔlioc Sto sunèdrio autì parousðasa ergasða me tðtlo: Minimal Lattice-Subspaces and Positive Bases. 34. Ebdomo Panell nio Sunèdrio Anˆlushc (Panep. KÔprou, Aprilioc 1999). S- to sunèdrio autì parousðase ergasða me tðtlo: Efarmog twn Sundèsmwn- Upoq rwnsth Majhmatik OikonomÐa. 35. Conference on Real Analysis and Measure Theory, Maiory, Italy, Sto sunèdrio autì parousðase ergasða me tðtlo: Minimal Lattice-Subspaces. 36. Pèmto Panell nio Sunèdrio Anˆlushc (An geia, Sept ) Sto sunèdrio autì parousðase ergasða me tðtlo: Elˆqistoi SÔndesmoi-Upìqwroi. 37. Conference on Real Analysis and Measure Theory, Ischia, Italy, IoÔlioc Sto sunèdrio autì parousðase ergasða me tðtlo: Minimal Lattice-Subspaces. 38. Current trends in economics and labor markets effects Kefalloniˆ Mˆðoc Sto sunèdrio autì parousðase ergasða me tðtlo: Lattice-Subspaces of C(Ω). 39. Conference on Real Analysis and Measure Theory, Ischia, Italy, IoÔnioc Sto sunèdrio autì parousðase ergasða me tðtlo: Lattice-Subspaces of C(Ω). 40. Tètarto Panell nio Sunèdrio Anˆlushc (Panepist mio Patr n, Sept. 1994) Sto sunèdrio autì parousðase ergasða me tðtlo: Diatetagmènoi upìqwroi tou C[0, 1]. 41. Sunèdrio Germanik c Majhmatik c EtairÐac, Linz, AustrÐa, Septèmbrioc Sto sunèdrio autì parousðase apì koinoô me ton D. KrabbarÐth ergasða me tðtlo: Weakly compact subsets of L 1 (µ, X). 42. Current trends in economics and labor markets effects, Kefalloniˆ Mˆðoc Sto sunèdrio autì parousðase apì koinoô me ton Yuri Abramovich ergasða me tðtlo: Lattice-Subspaces in Economic Theory. 43. Sunèdrio Germanik c Majhmatik c EtairÐac, BerolÐno, Septèmbrioc Sto sunèdrio autì parousðase ergasða me tðtlo: Cones with the Radon-Nikodym property. 44. DeÔtero Panell nio Sunèdrio Anˆlushc (Panepist mio Ajhn n, Febrouˆrioc 1992). Sto sunèdrio autì parousðase ergasða me tðtlo: H idiìthta Radon- Nikodym se diatetagmènouc q rouc. 45. Pr to Panell nio Sunèdrio Anˆlushc (Aristotèleio Panepist mio, JessalonÐkh, Septèmbrioc 1990.) Sto sunèdrio autì parousðasa ergasða me tðtlo: Bˆseic Schauder se diatetagmènouc upoq rouc tou C([0, 1]). 46. Diejnèc sumpìsio jewrðac Telest n (EMP AÔgoustoc 1985). Sto sunèdrio autì parousðase ergasða me tðtlo:: Cones locally-isomorphic to the positive cone of l 1 (Γ). 5

6 47. 'Ebdomo Sunèdrio thc Balkanik c 'Enwshc Majhmatik n (EMP Dekèbrioc 1983). Sto sunèdrio autì parousðase ergasða me tðtlo: Strongly exposed points in a base for a cone. DIALEXEIS 'Eqw prosklhjeð kai èqei d sei tic parakˆtw dialèxeic: 1. IoÔnioc 2011: Lattice-subspaces and applications finance, University of Napoli, Federico II, Italy. 2. Martioc 2011: Lattice-subspaces and applications in linear optimization, Catholic University of Milan, Italy : Cones and Geometry of Banach spaces., Istanbul Seminar of Analysis, Turkey : Lattice-subspaces and positive bases., Seminar of Analysis, Department of Mathematics, Adam Mickiewicz university, Poznan, Poland : Demand functions and reflexivity, Universitat Wien, Institut fur Volkswirtschaftslehre : Sunart seic Z thshc kai Qarakthrismìc thc anaklastikìthtac, Seminˆrio tou tomèa Genik c Oikonomik c JewrÐac kai Politik c tou Tm - matoc Oikonomik n Episthm n tou A.P.J : JewrÐa thc Oikonomik c IsorropÐac, Seminˆrio Efarmosmènhc Anˆlushc tou MajhmatikoÔ tm matoc tou PanepisthmÐou Patr n. 8. Febrouˆrioc 2002: Minimum cost portfolio insurance, Seminˆrio tou DiapanepisthmiakoÔ DidaktorikoÔ Progrˆmmatoc Spoud n, tou OikonomikoÔ PanepisthmÐou Ajhn n kai tou OikonomikoÔ Tm matoc tou PanepisthmÐou A- jhn n. 9. Minimum cost portfolio insurance, Department of Management, Purdue University, Ianouˆrioc Lattice-Subspaces and geometry of Banach lattices, Bucharest October The Structure of Lattice-Subspaces, Department of Mathematics Univ. Complutense, Madride, January Minimal Lattice-Subspaces,Department of Mathematics IUPUI, The Structure of Lattice-Subspaces, Department of Mathematics IUPUI, Upìqwroi diatetagmènwn q rwn Banach, Majhmatikì tm ma, Panepist - mio AigaÐou, Upìqwroi diatetagmènwn q rwn Banach, Seminˆrio Anˆlushc, Majhmatikì Tm ma, Panepist mio Ajhn n The Radon-Nikodym Property in Ordered Banach Spaces, Seminˆrio Anˆlushc, Department of Mathematics, University of Missouri, Mˆðoc The Radon-Nikodym Property in Ordered Banach Spaces, Department of Mathematics IUPUI, AprÐlioc

7 18. H Idiìthta Radon-Nikodym kai efarmogèc thc sto qarakthrismì q rwn Banach, Seminˆrio MajhmatikoÔ Tm matoc tou PanepisthmÐou Patr n,

8 DHMOSIEUSEIS SE EPISTHMONIKA PERIODIKA 1. C. Kountzakis, I. Polyrakis, Coherent Risk Measures in general Economic models and Price Bubbles, Journal of Mathematical Economics,(in Press). 2. E. Casini, E. Miglierina, I. Polyrakis, F. Xanthos, Reflexive Cones, Positivity Vol.17 Is.3 (2013) I. Polyrakis, F. Xanthos Grothendieck ordered Banach spaces with an interpolation Property, Proc. Amer. Math. Soc., (in Press). 4. B. Katsikis and I. Polyrakis, Computation of vector sublattices and minimal lattice-subspaces of R k, Applications in Finance. Applied Mathematics and Computation, Vol. 218, Is. 12 (2012) I. Polyrakis, F. Xanthos Cone characterization of Grothendieck spaces and Banach spaces containing c 0, Positivity, Vol.15 (2011) C. Kountzakis, I. Polyrakis, F. Xanthos, Non-replicated options, Mathematical Finance doi: /j x I. Polyrakis, F. Xanthos, Maximal submarkets that replicate any option, Annals of Finance, (2011)7: (online) 8. B. Katsikis and I. Polyrakis, Positive Bases in ordered subspaces with the Riesz decomposition property Studia Mathematica 174 (2006) I. Polyrakis, Demand functions and reflexivity Journal of Mathematical Analysis and Applications, 338, Issue 1, (2008) C. Kountzakis and I. Polyrakis The completion of security markets Decisions in Economics and Finance, 29 (2006) C. Kountzakis and I. Polyrakis Geometry of cones with applications in the Existence of Pareto efficient points, Journal of Mathematical Analysis and Applications, 320 (2006) I. A. Polyrakis, A characterization of l + 1 (2004), no. 2, (Γ), Quaestiones Mathematicae, I. A. Polyrakis Cones and Geometry of Banach spaces. Atti Sem. Mat. Fis. Univ. Modena, LII (2004) I. A. Polyrakis, Embeddability of L 1 (µ) in dual spaces and a characterization of c 0, Journal of Mathematical Analysis and Applications, 289,(2004) I. A. Polyrakis, The Structure of Lattice-Subspaces Positivity 7 (2003), no. 1-2, I. A. Polyrakis, Lattice-subspaces and Positive Bases in Function Spaces, Positivity 7 (2003), no. 4, I. A. Polyrakis, Linear Optimization in C(Ω) and portfolio insurance, Optimization, Vol.52, No.2 (2003) C. D. Aliprantis I. Polyrakis and R. Tourky, The Cheapest Hedge, Journal of Mathematical Economics, Volume 37, Issue 4 (2002) I. A. Polyrakis, Lattice-subspaces and Positive Bases. An Application in E- conomics, Atti Sem. Mat. Fis. Univ. Modena, volume L, (2002), no. 2,

9 20. I. A. Polyrakis, Bases for cones and reflexivity in Banach spaces, Quaestiones Mathematicae, 24 (2001) I. A. Polyrakis, Spaces with dual order-isomorphic to l 1, Positivity, 4 (2000) I. A. Polyrakis, Minimal lattice-subspaces, Transactions of the American Mathematical Society, 351 (1999) C. D. Aliprantis and D. Brown and I. Polyrakis and J. Werner, Portfolio Dominance and Optimality in Infinite Security Markets, Journal of Mathematical Economics, 30 (1998) C. D. Aliprantis, D. Brown, I. Polyrakss and J. Werner, Yudin Cones and Inductive Limits Topologies, Atti Sem. Mat. Fis. Univ. Modena, volume XLVI, (1998) I. A. Polyrakis, Finite-dimentional lattice-subspaces of C(Ω) and curves of R n, Transactions of the American Mathematical Society, 348, no 7 (1996) Y. A. Abramovich, C. D. Aliprantis and I. A. Polyrakis, Some Remarks on Surjective and Bounded Below Operators Atti Sem. Mat. Fis. Univ. Modena, volume XLIV (1996) I. A. Polyrakis, Cone characterization of reflexive Banach lattices, Glaskov Math. Journal,37 (1995) I. A. Polyrakis, The Radon-Nikodým Property in Ordered Banach Spaces, Journal of Mathtical Analysis and Applications, 192 (1995) Y. A. Abramovich and C. D. Aliprantis and I. A. Polyrakis, Iattice-subspaces and positive projections, Proc. R. Ir. Acad. 14 A, number 2 (1994) N. Hadjisavvas, D. Kravvaritis, I. Polyrakis, Weakly compact Subspaces of L 1 (µ, X) and bvca(σ, X), Rendiconti del Circolo Matematico di Palermo, Serie II, Volume XLIII (1994) I. A. Polyrakis, Lattice-subspaces of C[0, 1] and positive bases, Journal of Mathematical Analysis and Applications, 184 (1991) N. Hadjisavvas, D. Kravvaritis, G. Pantelidis and I. Polyrakis, Hereditary Order Convexity in L(X, Y ), Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo XXXVIII (1985) N. Hadjisavvas, D. Kravvaritis, G. Pantelidis and I. Polyrakis, Nonlinear monotone operators with Values in L(X, Y ), Journal of Mathematical Analysis and its Applications, 140 (1989) No 1, I. A. Polyrakis, Cones locally isomorphic to the positive cone of l 1 (Γ), Linear Algebra and Its Applications, 44 (1986) I. A. Polyrakis, Strongly exposed points and a characterization of l 1 (Γ) by the Schur Property, Proceedings Edinburgh Mcthematical Society, 36, (1986) I. A. Polyrakis, Schauder bases in locally solid lattice Banach spaces, Mathematical Proceedings Cambridge Philosophical Society 101,(1987) I. A. Polyrakis, Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterization of l 1 (Γ), Proceedings Edinburgh Mathematical Society, 29,(1972)

10 38. I. A. Polyrakis, Extreme points of unbounded, closed and convex sets in Banach spaces, Mathematical Proceedings Cambridge Philosophical Society 95 (1984) I. A. Polyrakis, Lattice Banach spaces order-isomorphic to l 1, Mathematical Proceedings Cambridge Philosophical Society 44,(1983) ANAFORES Sth mhqan anaz thshc google scholar upˆrqoun 225 anaforèc. 10