Research Article

Pelczyński’s property (V) and (V∗) on tensor products and spaces of compact operators

Published in: Quaestiones Mathematicae
Volume 49 , issue 1 , 2026 , pages: 71–78

DOI: 10.2989/16073606.2025.2551750

Author(s): Qingying Bu University of Mississippi, University, USA

Keywords: Primary: 46B28 , Secondary: 46M05 , Tensor product , space of compact operators , Pelczyński’s property (V)

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Abstract

Let U be a reflexive Banach space with an unconditional basis and X be any Banach space. We show that if X has Pelczyński’s property (V) then (U,X) has Pelczyński’s property (V). We also show that if X has Pelczyński’s property (V∗) then (i) X

Y has Pelczyński’s property (V∗), and (ii) (U,X) has Pelczyński’s property (V∗) if and only if every bounded linear operator from U to X is compact. As an application, we provide new examples of non-reflexive Banach spaces with Pelczyński’s property (V) and Pelczyński’s property (V∗), respectively.

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