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Operators from certain Banach spaces to Banach spaces of cotype $q\ge 2$

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Abstract

Suppose {X_n}_{n=1}^infty is a sequence of finite dimensionalBanach spaces and suppose that X is either a closed subspace of(sum_{n=1}^infty X_n)_{c_0} or a closed subspace of(sum_{n=1}^infty X_n)_p with p > 2. We show that everybounded linear operator from X to a Banach space Y of cotypeq (2 le q < p) is compact.

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