Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-23T23:26:57.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Markuševič Bases and Corson Compacta in Duality

Published online by Cambridge University Press:  20 November 2018

J. Vanderwerff ,
J. H. M. Whitfield  and
V. Zizler
J. Vanderwerff
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G
J. H. M. Whitfield
Affiliation:
Department of Mathematical Sciences Lakehead University Thunder Bay, Ontario P7B 5E1
V. Zizler
Affiliation:
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1
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 characterize Banach spaces that admit Markuševič bases with various properties connected with weak countable determining or weak Lindelöf determining of spaces or with various norming properties.

Keywords

46B20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 1 , 01 February 1994 , pp. 200 - 211
Copyright
Copyright © Canadian Mathematical Society 1994

References

[AP] Alster, K. and Pol, R., On function spaces on compact subspaces ofL-products of the real line, Fund. Math. 107(1980), 135–143.Google Scholar
[AL] Amir, D. and Lindenstrauss, J., The structure of weakly compact sets in Banach spaces, Ann. of Math. 88(1968), 35–46.Google Scholar
[AM] Argyrosand, S. Mercouvakis, S., On weakly Lindelof Banach spaces, Rocky Mount. J. Math. 23(1993), 395–446.Google Scholar
[C] Corson, H. H., Normality in subsets of product spaces, Amer. J. Math. 81(1959), 785–796.Google Scholar
[DG] Deville, R. and Godefroy, G., Some applications of projectional resolutions of identity, Proc. London Math. Soc. 67(1993), 183–199.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(1993).Google Scholar
[FaG] Fabian, M. and Godefroy, G., The dual of every Asplund space admits a projectional resolution of identity, StudiaMath. 91(1988), 141–151.Google Scholar
[FG] Finet, C. and Godefroy, G., Biorthogonal systems and big quotient spaces, Contemporary Mathematics 85(1989), 87–110.Google Scholar
[G] Godefroy, G., Asplund spaces and decomposable nonseparable Banach spaces, Rocky Mount. J. Math., to appear.Google Scholar
[GoT] Godun, B. V. and Troyanski, S. L., Norm attaining operators and the geometry of the unit sphere of a Banach space, Soviet Math. Dokl. 42(1991), 532–534.Google Scholar
[JZ] John, K. and Zizler, V., Some notes on Markusevic bases in weakly compactly generated Banach spaces, Compositio Math. 35(1977), 113–123.Google Scholar
[JL] Johnson, W. B. and J. Lindenstrauss, Some remarks on weakly compactly generated Banach spaces, Israel J. Math. 17(1974), 219–230.Google Scholar
[LT] Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces. I. Sequence spaces, Springer-Verlag, 1977.Google Scholar
[M] Mercourakis, S., On weakly countably determined Banach spaces, Trans. Amer. Math. Soc. 300 (1987), 307–327.Google Scholar
[NP] Namioka, I. and Phelps, R. R., Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), 735–750.Google Scholar
[N] Negrepontis, S., Banach spaces and topology, Handbook of Set-Theoretic Topology, 1984, 1045–1142.Google Scholar
[OSV] Orihuela, J., Schachermayer, W. and Valdivia, M., Every Radon-Nikodym Corson compact is Eberlein ompact, Studia Math. 98( 1991 ), 157–174.Google Scholar
[P1] Plicko, A. N., Some properties of Johnson-Lindenstrauss space, Functional Anal. Appl. 15(1981), 149–150.Google Scholar
[P2] Plicko, A. N., On projective resolutions of the identity operator and Markusevic bases, Soviet Math. Dokl. 25(1982), 386–389.Google Scholar
[Pol] Pol, R., On a question of Corson H. H. and some related problems, Fund. Math. 109(1980), 143–154.Google Scholar
[Po2] Pol, R., On pointwise and weak topology in function spaces, Warsaw University, 1984, preprint.Google Scholar
[S] Singer, I., Bases in Banach spaces II, Springer-Verlag, Berlin-Heidelberg-New York, 1981.Google Scholar
[VI] Valdivia, M., Resolutions of identity in certain Banach spaces, Collect. Math. 39(1988), 127–140.Google Scholar
[V2] Valdivia, M., Resolucionesproyectivas del operador identidady bases de Markushevich en ciertos espacios de Banach, Rev. Real Acad. Cienc. Exact. Ffs. Natur. Madrid 84(1990), 23–34.Google Scholar
[V3] Valdivia, M., Simultaneous resolutions of the identity operator in normed spaces, Collect. Math. 42( 1991 ), 265–284.Google Scholar
[V4] Valdivia, M., On certain class of Markushevich bases, preprint.Google Scholar
[Va] Vanderwerff, J., Extensions of Markusevic bases, to appear.Google Scholar