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

Ghoussoub, N.; Maurey, B.; Schachermayer, W.

doi:10.1090/S0002-9939-1987-0870785-2

A counterexample to a problem on points of continuity in Banach spaces
HTML articles powered by AMS MathViewer

by N. Ghoussoub, B. Maurey and W. Schachermayer

Proc. Amer. Math. Soc. 99 (1987), 278-282

DOI: https://doi.org/10.1090/S0002-9939-1987-0870785-2

PDF | Request permission

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

J. Bourgain and H. P. Rosenthal, Applications of the theory of semi-embeddings to Banach space theory, J. Funct. Anal. 52 (1983), no. 2, 149–188. MR 707202, DOI 10.1016/0022-1236(83)90080-0
J. Bourgain, Dentability and finite-dimensional decompositions, Studia Math. 67 (1980), no. 2, 135–148. MR 583294, DOI 10.4064/sm-67-2-135-148
G. A. Edgar and R. F. Wheeler, Topological properties of Banach spaces, Pacific J. Math. 115 (1984), no. 2, 317–350. MR 765190
N. Ghoussoub and B. Maurey, $G_\delta$-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), no. 1, 72–97. MR 779739, DOI 10.1016/0022-1236(85)90039-4
J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain $\ell _{1}$ and whose duals are non-separable, Studia Math. 54 (1975), no. 1, 81–105. MR 390720, DOI 10.4064/sm-54-1-81-105