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International Journal of Mathematics and Mathematical Sciences
Volume 4 (1981), Issue 1, Pages 39-53
http://dx.doi.org/10.1155/S0161171281000021

Mazur spaces

Department of Mathematics #14, Lehigh University, Bethlehem 18015, Pennsylvania, USA

Received 3 October 1979

Copyright © 1981 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is settled: the dual space need not be Mazur.