Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T17:04:22.456Z Has data issue: false hasContentIssue false
  • English
  • Français

Biorthogonal Systems in Weakly Lindelöf Spaces

Published online by Cambridge University Press:  20 November 2018

M. Fabian ,
V. Montesinos  and
V. Zizler
M. Fabian
Affiliation:
Mathematical Institute of the Czech Academy of Sciences, Žitná 25, 11567, Prague 1 Czech Republic e-mail: [email protected]
V. Montesinos
Affiliation:
Departamento de Matemática Aplicada, E.T.S.I. Telecommunicación, Universidad Politécnica de Valencia, C/Vera, s/n. 46071 Valencia, Spain e-mail: [email protected]
V. Zizler
Affiliation:
Department of Mathematical Sciences, University of Alberta, 632 Central Academic Building, Edmonton, Alberta, T6G 2G1 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study countable splitting of Markushevich bases in weakly Lindelöf Banach spaces in connection with the geometry of these spaces.

Keywords

46B0346B2046B26Weak compactnessprojectional resolutionsMarkushevich basesEberlein compactsVašák spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 1 , 01 March 2005 , pp. 69 - 79
Copyright
Copyright © Canadian Mathematical Society 2005

References

[AL] Amir, D. and Lindenstraus, J.,. The structure of weakly compact sets in Banach spaces. Ann. of Math. 88(1968), 35–46.Google Scholar
[BRW] Benyamini, Y., Rudin, M. E. and Wage, M., Continuous images of weakly compact subsets of Banach spaces. Pacific J. Math. 70(1977), 309–324.Google Scholar
[CL] Corson, H. H. and Lindenstrauss, J., On weakly compact subsets of Banach spaces. Proc. Amer. Math. Soc 17(1966), 476–48.Google Scholar
[DGZ] Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces. Pitman Monographs and Surveys in Pure and Applied Mathematics, 64, Longman Scientific and Technical, 1993.Google Scholar
[D] Diestel, J., Geometry of Banach spaces, Selected topics. Lecture Notes in Math. 485, Springer-Verlag, Berlin, 1975.Google Scholar
[F] Fabian, M., Gâteaux differentiability of convex functions and topology.Weak Asplund spaces. Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley and Sons, New York, 1997.Google Scholar
[F2] Fabian, M., Habala, P., Hájek, P., Montesinos, V., Pelant, J. and Zizler, V., Functional analysis and infinite dimensional geometry. CMS. Books in Mathematics 8, Springer-Verlag, New York, 2001.Google Scholar
[FMZ1] Fabian, M., Montesinos, V. and Zizler, V., Pointwise semicontinuous smooth norms. Arch. Math. Base. 78(2002), 459–464.Google Scholar
[FMZ2] Fabian, M., Montesinos, V. and Zizler, V., A characterization of subspaces of weakly compactly generated Banach spaces, J. London Math. Soc. 69(2004), 457–464.Google Scholar
[Fa] Farmaki, V., The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ(ℝΓ) Funda. Math. 128(1987), 15–28.Google Scholar
[G] Godefroy, G., Asplund spaces and decomposable Banach spaces. Rocky Mountain J. Math. 25(1995), 1013–1024.Google Scholar
[Gu] Gul’ko, S. P., On properties of subsets of Σ-products. Soviet Math. Dokl. 18(1977), 1438–1442.Google Scholar
[JZ] John, K. and Zizler, V., Some notes on Markuševič bases in weakly compactly generated Banach spaces. Compositio Math. 35(1977), 113–123.Google Scholar
[JZ1] John, K. and Zizler, V., Smoothness and its equivalents in weakly compactly generated Banach spaces. J. Functional Analysi. 15(1974), 1–11.Google Scholar
[MR] Michael, E. and Rudin, M. E., A note on Eberlein compacts. Pacific J. Math. 72(1977), 487–495.Google Scholar
[N] Namioka, I., Separate continuity and joint continuity. Pacific J. Math. 51(1974), 515–531.Google Scholar
[NT] Negrepontis, S. and Tsarpalias, A., A non-linear version of the Amir-Lindenstrauss method. Israel J. Math. 38(1981), 82–94.Google Scholar
[O] Orihuela, J., On weakly Lindel¨of Banach spaces. Progress in Functional Analysis, (Bierstedt, K.D., Bonet, J., Horvath, J. and Maestre, M., eds.), Elsevier, Amsterdam, 1992.Google Scholar
[R] Rosenthal, H.P., The heredity problem for weakly compactly generated Banach spaces. Compositio Math. 28(1974), 83–111.Google Scholar
[S] Sokolov, G. A., On some class of compact spaces lying in Σ-products, Comment.Math. Univ. Carolin. 25(1984), 219–231.Google Scholar
[V] Valdivia, M., Simultaneous resolutions of the identity operator in normed spaces. Collect. Math. 42(1991), 265–284.Google Scholar
[VWZ] Vanderwerff, J., Whitfield, J. H. M. and Zizler, V., Markuševič bases and Corson compacta in duality. Canad. J. Math. 46(1994), 200–211.Google Scholar
[Z] Zizler, V.. Nonseparable Banach spaces, Handbook of the Geometry of Banach spaces Vol II, North-Holland, Amsterdam, 2003.Google Scholar