Tightness of Banach spaces and Baire category

Details Tightness of Banach spaces and Baire category Tightness of Banach spaces and Baire category

2011-11-28

arxiv.org/abs/1111.6444v1

Mathematics

Functional Analysis

13 pages

Scientific paper

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.

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