On complemented copies of c₀(ω₁) in C(Kⁿ) spaces
Given a compact Hausdorff space K we consider the Banach space of real continuous functions C(Kⁿ) or equivalently the n-fold injective tensor product or the Banach space of vector valued continuous functions C(K,C(K,C(K...,C(K)...). We address the question of the existence of complemented copies of c₀(ω₁) in under the hypothesis that C(K) contains such a copy. This is related to the results of E. Saab and P. Saab that contains a complemented copy of c₀ if one of the infinite-dimensional Banach...