Tightness of Banach spaces and Baire category

2011/11/28 by Ferenczi, Valentin, Godefroy, Gilles
#46B20 #54E52 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1111.6444

Abstract

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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