Biorthogonal systems and quotient spaces via baire category methods

Mathematische Annalen

Volumn 335, Issue 3, 2006, Pages 687-715

  Todorcevic, Stevo ^a,b  

^a UNIVERSITY OF TORONTO   (Canada)

^b CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33744724365     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-006-0762-7     Document Type: Article

References (40)

1. [B] Banach, S.: Théorie des opérations linéaires, Warszawa 1932
2. [BL] Benyamini, Y., Lindenstrauss, J.: Geometric Nonlinear Functional Analysis. Amer. Math. Soc., Providence 2000
3. [BGT] Bell, M., Ginsburg, J., Todorcevic, S.: Countable spread of exp Y and λY. Topology and its Appl. 14, 1-12 (1982)
4. [BV] Borwein, J.M., Vanderwerff, J.D.: Banach spaces that admit support sets. Proc. Amer. Math. Sac. 124, 751-755 (1996)
5. [DJ] Davis, W.J., Johnson, W.B.: On the existence of fundamental and total bounded biorthogonal systems in Banach spaces. Studia Math. 45, 173-179 (1972)
6. [E] Engelking, R.: General Topology, Heldermann Verlag Berlin 1989
7. [F-Z] Fabian, M., Habala, P., Hajek, P., Montesinos, V., Pelant, J., Zizler, V.: Functional Analysis and Infinite-Dimensional Geometry. CMS Books in Mathematics, Springer-Verlag, 2001
8. [FG] Finet, C., Godefroy, G.: Biorthogonal systems and big quotient spaces. Contemp. Math. 85, 275-283 (1989)
9. [FMS] Foreman, M., Magidor, M., Shelah, S.: Martin's maximum, saturated ideals and non-regular ultrafilters. Ann. Math. 127, 1-47 (1988)
10. [F] Fremlin, D.H.:Consequences of Martin's axioms. Cambridge Univ. Press 1984
11. [Fr] Frontisi, J.: Lissité et dialité dans les espaces de Banach. Thése de Dectorat, Univ. Paris VI, 1996
12. [GL] Godefroy, G., Louveau, A.: Axioms of determinacy and biorthogonal systems. Israel J.Math. 67, 109-116 (1989)
13. [GT] Grodefroy, G., Talagrand, M.: Espaces de Banach representables. Israel J. Math. 41, 321-330 (1982)
14. [GK] Godun, B.V., Kadets, M.: Banach spaces without complete minimal systems. Funk. Analiz i Ego Pril. 14, 67-68 (1980)
15. [J1] Johnson, W.B.: No infinite dimensional P space admits a Markushevich basis. Proc. Amer. Math. Soc. 28, 467-468 (1970)
16. [J2] Johnson, W.B.: E-mail message of November 16, 2005
17. [JR] Johnson, W.B., Rosenthal, H.P.: On ω*-basic sequences and their applications in the study of Banach spaces. Studia Math. 43, 77-92 (1972)
18. [Ko] Koszmider, P.: A problem of Rolewics about Banach spaces that admit support sets, preprint 2004
19. [Ku1] Kunen, K.: Products of S-spaces, note of May 1975
20. [Ku2] Kunen, K.: On hereditarily Lindelof Banach spaces, note of July 1980
21. [Kt] Kutzarova, D.: Convex sets containing only support points in Banach spaces with an uncountable minimal system. C.R. l'Acad. Bulg. Sci., 39, 13-14 (1986)
22. [L] Lazar, A.J.: Points of support for closed convex sets. Illinois J. Math. 25, 302-305 (1981)
23. [LT] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces, I, Springer-Verlag, Berlin, 1977
24. [Mu] Mujica, J.: Separable quotients of Banach spaces. Revista Mat. Univ. Complut. 10, 299-330 (1997)
25. [M] Montesinos, V.: Solution to a problem of S. Rolewicz. Studia Math. 81, 65-69 (1985)
26. [N] Negrepontis, S.: Banach spaces and topology, Handbook of Set-Theoretic topology. In: Kunen, K., Vaughan, J.E., (eds), North-Holland, 1984, pp. 1045-1142
27. [P] Pelczynski, A.: Some problems on basis in Banach and Fréchet space. Israel J. Math. 2, 132-138 (1964)
28. [Pl2] Plichko, A.N.: Fundamental biorthogonal systems and projective bases in Banach spaces. Math. Zametki 34, 473-476 (1983)
29. [Pl1] Plichko, A.N.: Banach spaces without fundamantal biorthogonal systems. Soviet Math. Dokl. 254(4), 978-801 (1980)
30. [R] Rolewicz, S.: On convex sets containing only points of support. Comment. Math., Prace Math. Special issue 1, 279-281 (1978)
31. [Si] Singer, I.: Bases in Banach spaces II, Springer-Verlag, Berlin, 1981
32. [Sh] Shelah, S.: Uncountable constructions for BA, e.g. groups and Banach spaces. Israel J.Math. 51, 273-297 (1985)
33. [T1] Todorcevic, S.: Forcing positive partition relations. Trans. Amer. Math. Soc. 280, 703-720 (1983)
34. [T2] Todorcevic, S.: Directed sets and cofinal types. Trans. Amer. Math. Soc. 290, 711-723 (1985)
35. [T3] Todorcevic, S.: Partition problems in topology, Amer. Math. Soc. Providence 1989
36. [T4] Todorcevic, S.: Irredundant sets in Boolean algebras. Trans. Amer. Math. Soc. 339, 35-44 (1990)
37. [T5] Todorcevic, S.: Some applications of S and L combinatorics. Ann. New York Acad. Sci., 705, 130-167 (1993)
38. [T6] Todorcevic, S.: Basis problems in combinatorial set theory, Proc. International Congress of Mathematicians Berlin 1998, Docum. Math. Extra Volume ICM 1998. II. 43-52
39. [T7] Todorcevic, S.: A generic function space C(K) with no support set, in preparation
40. [W] Wojtaszczyk, P.: A theorem on convex sets related to the abstract Pontriagin maximality principle. Bull. Acad. Polon Sci 21, 93-95 (1973)