Remarks on a theorem of Taskinen on spaces of continuous functions

Abstract

We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(K-n), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n is an element of N, the symmetric injective n-tensor product of C(K)(⊗) over cap C-n(s,epsilon)(K), is complemented in C((BC(K)*)), a result of independent interest. The techniques we develop allow us to extend the result in several directions. We also show that the hypothesis of metrizability and uncountability cannot be removed