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

Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 53-56 Printed March 1, 2002

Chong-Man Cho Hanyang University

Abstract : Suppose $\{X_n\}_{n=1}^\infty$ is a sequence of finite dimensional Banach 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 every bounded linear operator from $X$ to a Banach space $Y$ of cotype $q$ $(2 \le q < p)$ is compact.