COMPLEMENTED COPIES OF c_0(τ) IN TENSOR PRODUCTS OF L_p[0, 1]

摘要

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 L_p([0, 1], X) or the injective tensor product L_p[0, 1]^?_εX contains a complemented copy of c_0(τ), then so does X. We show also that if p?(1,∞) and the projective tensor product L_p[0, 1]^?πX contains a complemented copy of c_0(τ), then so does X.