Vol. 301, No. 1, 2019

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Complemented copies of $c_0(\tau)$ in tensor products of $L_p[0,1]$

Vinícius Morelli Cortes, Elói Medina Galego and Christian Samuel

Vol. 301 (2019), No. 1, 67–88
DOI: 10.2140/pjm.2019.301.67
Abstract

Let X be a Banach space and τ an infinite cardinal. We show that if τ has uncountable cofinality, p [1,), and either the Lebesgue–Bochner space Lp([0,1],X) or the injective tensor product Lp[0,1]̂εX contains a complemented copy of c0(τ), then so does X. We show also that if p (1,) and the projective tensor product Lp[0,1]̂πX contains a complemented copy of c0(τ), then so does X.

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