Copies of c_0(τ) in Saphar tensor products - Cortes, Vinícius Morelli (MATHEMATICA SCANDINAVICA, 2022)
Let X, Y be Banach spaces, τ an infinite cardinal and 1 ≤ p < ∞ . We extend a result by E. Oja by showing that if X has a boundedly complete unconditional basis and either X _g_p Y or X _ε _p Y contains a complemented copy of c_0(τ ), then Y contains a complemented copy of c_0(τ ). We show also that if α is a uniform crossnorm, X _α Y contains a (complemented) copy of c_0(τ ) and the cofinality of τ is strictly greater than the density of X, then Y also contains a (complemented) copy of c_0(τ ). As an application, we obtain a result concerning complemented copies of _1(τ ) in X _α Y.