arXiv:1111.6444 Abstract | arXiv Analytics

arXiv:1111.6444 [math.FA]Abstract References Reviews Resources

Tightness of Banach spaces and Baire category

Published 2011-11-28Version 1

We prove several dichotomies on linear embeddings between Banach spaces. Given an arbitrary Banach space X with a basis, we show that the relations of isomorphism and bi-embedding are meager or co-meager on the Polish set of block-subspaces of X. We relate this result with tightness and minimality of Banach spaces. Examples and open questions are provided.

Comments: 13 pages

Categories: math.FA

Subjects: 46B20, 54E52

Keywords: baire category, arbitrary banach space, linear embeddings, open questions, isomorphism

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