Uniform Kadec-Klee Property in Banach lattices

1994/06/06 by Fouad Chaatit, Chaatit, Fouad, Mohamed A. Khamsi +1
Mathematics · #46B #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.math/9406209

openalex publication_date 1994/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Banach lattice X which does not contain the lⁿ_∞-uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology τ on X. In case the Banach lattice is purely atomic, the topology τ is the coordinatewise convergence topology.

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