Banach spaces for which the space of operators has 2^{\mathfrak c} closed ideals

2020/06/27 by Freeman, Daniel, Schlumprecht, Thomas, Zsak, Andras
#47B37 #FOS: Mathematics #Functional Analysis (math.FA) #primary: 47L20 secondary 47B10

paper · doi:10.48550/arxiv.2006.15415

Abstract

We formulate general conditions which imply that L(X,Y), the space of operators from a Banach space X to a Banach space Y, has 2^{\mathfrak c} closed ideals where \mathfrak c is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson type spaces. In particular, we prove that the cardinality of the set of closed ideals in L(ℓ_p⊕ℓ_q) is exactly 2^{\mathfrak c} for all 1

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