A version of Kalton's theorem for the space of regular operators

2013/10/06 by Foivos Xanthos, Xanthos, Foivos
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1310.1591

openalex publication_date 2013/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we extend some recent results in the space of regular operators. In particular, we provide the following Banach lattice version of a classical result of Kalton: Let E be an atomic Banach lattice with an order continuous norm and F a Banach lattice. Then the following are equivalent: (i) L^r(E,F) contains no copy of ℓ_∞, (ii) L^r(E,F) contains no copy of c₀, (iii) K^r(E,F) contains no copy of c₀, (iv) K^r(E,F) is a (projection) band in L^r(E,F), (v) K^r(E,F)=L^r(E,F).

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