On convexity and compactness
in F-spaces with bases

Joel H. Shapiro


Indiana Univ. Math. J. 21 1073--1090
Abstract: I characterize the F-spaces with "absolute" bases which have the property that no infinite dimensional linear subspace is locally convex. In the other direction I show that there exist F-spaces that are not locally convex but have the property that every infinite dimensional subspace contains an infinite dimensional locally convex subspace.
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