Complemented copies of c0(τ) in tensor products of Lp[0,1]

Let $X$ be a Banach space and $τ$ an infinite cardinal. We show that if $τ$ has uncountable cofinality, $p \in [1, \infty)$ , and either the Lebesgue–Bochner space $L_{p} ([0, 1], X)$ or the injective tensor product $L_{p} [0, 1] {\hat{\otimes}}_{ε} X$ contains a complemented copy of $c_{0} (τ)$ , then so does $X$ . We show also that if $p \in (1, \infty)$ and the projective tensor product $L_{p} [0, 1] {\hat{\otimes}}_{π} X$ contains a complemented copy of $c_{0} (τ)$ , then so does $X$ .

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Keywords

$c_0(\Gamma)$ spaces, injective tensor products, projective tensor products, Lebesgue–Bochner spaces $L_p([0,1],X)$, complemented subspaces

Mathematical Subject Classification 2010

Primary: 46B03, 46E15

Secondary: 46B25, 46E30, 46E40

Milestones

Received: 21 April 2018

Revised: 8 October 2018

Accepted: 18 October 2018

Published: 16 September 2019

Authors

Vinícius Morelli Cortes
Department of Mathematics University of São Paulo São Paulo Brazil

Elói Medina Galego
Department of Mathematics, IME University of São Paulo São Paulo Brazil

Christian Samuel
Aix Marseille Université, CNRS Marseille France

Vol. 301, No. 1, 2019

Vinícius Morelli Cortes, Elói Medina Galego and Christian Samuel

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors