Abstract
AbstractLet X be a Banach space, let I be an infinite set, let τ be an infinite cardinal and let . In contrast to a classical c0 result due independently to Cembranos and Freniche, we prove that if the cofinality of τ is greater than the cardinality of I, then the injective tensor product contains a complemented copy of if and only if X does. This result is optimal for every regular cardinal τ. On the other hand, we provide a generalization of a c0 result of Oja by proving that if τ is an infinite cardinal, then the projective tensor product contains a complemented copy of if and only if X does. These results are obtained via useful descriptions of tensor products as convenient generalized sequence spaces.
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