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Phelps spaces and finite dimensional decompositions

Published online by Cambridge University Press:  17 April 2009

R. Deville ,
G. Godefroy ,
D.E.G. Hare  and
V. Zizler
R. Deville
Affiliation:
Laboratoire de Mathematiques, Université de Franclme-Comté, and Université of Paris VI, Besancon, France
G. Godefroy
Affiliation:
Equipe d'aimalyse Fonctionnelle, Université of Paris VI, Paris, France
D.E.G. Hare
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, Canada
V. Zizler
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Canada
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Abstract

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We show that if X is a separable Banach space such that X* fails the weak* convex point-of-continuity property (C*PCP), then there is a subspace Y of X such that both Y* and (X/Y)* fail C*PCP and both Y and X/Y have finite dimensional Schauder decompositions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 263 - 271
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bourgain, J., ‘Dentabiity and finite dimensional decompositions’, Studia Math. 67 (1980), 135–148.CrossRefGoogle Scholar
[2]Bourgain, J., ‘Le proprieté de Radon–Nikodym’, Publications de l'université Pierre et Marie Curie, No. 36 (1979).Google Scholar
[3]Choquet, G., Lectures in Analysis (W.A. Benjamin, Inc., New York, 1969).Google Scholar
[4]Deville, R., Godefroy, G., Hare, D.E.G. and Zizler, V., ‘Differentiability of convex functions and the convex point of continuity property in Banach spaces’, Israel J. Math (to appear).Google Scholar
[5]Ghoussoub, N., Godefroy, G., Maurey, B. and Schachermayer, W., ‘Some topological and geometrical structures in Banach spaces’, (to appear).Google Scholar
[6]Ghoussoub, N., Maurey, B., ‘δ-embeddings in Hilbert spaces’, J. Funct. Anal. 81 (1985), 72–92.CrossRefGoogle Scholar
[7]Ghoussoub, N., Maurey, B., ‘δ-embeddings in Hubert space’, J. Funct. Anal. (to appear).Google Scholar
[8]Goussoub, N., Maurey, B. and Schachermayer, W., ‘Geometrical implications of certain infinite dimensional decompositions’, (to appear).Google Scholar
[9]Hare, D.E.G., ‘A dual characterization of Banach spaces with the convex point-of-continuity property’ (to appear).Google Scholar
[10]Johnson, W.B. and Rosenthal, H.P., ‘On ω*-basic sequences and their applications to the study of Banach spaces’, Studia Math. 43 (1972), 77–92.CrossRefGoogle Scholar
[11]Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces I: Sequence Spaces (Springer-Verlag, New York, 1977).CrossRefGoogle Scholar
[12]Luski, W., ‘A note on Banach spaces containing c0, or C∞,’, J. Funct. Anal. 62 (1985), 1–7.CrossRefGoogle Scholar
[13]Namioka, I. and Phelps, R.R., ‘Banach spaces which are Asplund spaces’, Duke Math. J. 42 (1975), 735–750.CrossRefGoogle Scholar
[14]Rosenthal, H.P., ‘A characterization of Banach spaces of Banach spaces containing ℓ’, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413.CrossRefGoogle ScholarPubMed
[15]Rosenthal, H.P., ‘ω*-Polish Banach spaces’, (to appear).Google Scholar
[16]Saab, B. and Saab, P., ‘A dual geometric characterization of Banach spaces not containing ℓ1’, Pacific J. Math., 105 (1983), 415–425.CrossRefGoogle Scholar
[17]Stegall, C., ‘The duality between Asplund spaces and spaces with the Radon-Nikodym property’, Israel J. Math 29 (1978), 408–412.CrossRefGoogle Scholar