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A counterexample to a problem on points of continuity in Banach spaces


Authors: N. Ghoussoub, B. Maurey and W. Schachermayer
Journal: Proc. Amer. Math. Soc. 99 (1987), 278-282
MSC: Primary 46B20; Secondary 46B10
DOI: https://doi.org/10.1090/S0002-9939-1987-0870785-2
MathSciNet review: 870785
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Abstract: In a previous paper of the first two authors [GM] the space $ J{T_\infty }$ was constructed as a James space over a tree with infinitely many branching points. It was proved that the predual $ {B_\infty }$ of $ J{T_\infty }$ fails the "point of continuity property."

In the present paper we show that $ {B_\infty }$ has the so-called "convex point of continuity property" thus answering a question of Edgar and Wheeler [EW] in the negative.


References [Enhancements On Off] (What's this?)

  • [BR] J. Bourgain and H. P. Rosenthal, Applications of the theory of semi-embeddings to Banach space theory, J. Funct. Anal. 52 (1983), 149-188. MR 707202 (85g:46018)
  • [B] J. Bourgain, Dentability and finite dimensional decompositions, Studia Math. 67 (1980), 135-148. MR 583294 (81m:46034)
  • [EW] G. A. Edgar and R. F. Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), 317-350. MR 765190 (86e:46013)
  • [GM] N. Ghoussoub and B. Maurey, $ {G_\delta }$-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), 72-97. MR 779739 (86m:46016)
  • [LS] J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain $ {l^1}$ and whose duals are not separable, Studia Math. 54 (1975), 81-105. MR 0390720 (52:11543)

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DOI: https://doi.org/10.1090/S0002-9939-1987-0870785-2
Article copyright: © Copyright 1987 American Mathematical Society

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