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Slicings, Selections and Their Applications

Published online by Cambridge University Press:  20 November 2018

N. Ghoussoub ,
B. Maurey  and
W. Schachermayer
N. Ghoussoub
Affiliation:
Department of Mathematics University of Bristish Columbia Vancouver, B.C. V6TIY4
B. Maurey
Affiliation:
U.F.R. de Mathématiques Université ParisVII 75251 Paris Cedex 05 France
W. Schachermayer
Affiliation:
Institut für Mathematik J. Kepler UniversitätA-4040 Linz Austria
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In the past few years, much progress have been made on several open problems in infinite dimensional Banach space theory. Here are some of the most recent results:

  1. 1) The existence of boundedly complete basic sequences in a large class of Banach spaces including the ones with the so-called Radon-Nikodym property ([G-M2], [G-M4]).

  2. 2) The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).

  3. 3) The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])

Keywords

46A5546B2049A27
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 3 , 01 June 1992 , pp. 483 - 504
Copyright
Copyright © Canadian Mathematical Society 1992

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