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
.