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Abstract
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Let
be a Banach space and
an infinite cardinal. We
show that if
has uncountable
cofinality,
, and either the
Lebesgue–Bochner space
or
the injective tensor product
contains a complemented copy of
,
then so does
. We show also
that if
and the projective
tensor product
contains
a complemented copy of
,
then so does
.
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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
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Mathematical Subject Classification 2010
Primary: 46B03, 46E15
Secondary: 46B25, 46E30, 46E40
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Milestones
Received: 21 April 2018
Revised: 8 October 2018
Accepted: 18 October 2018
Published: 16 September 2019
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