Commun. Korean Math. Soc. 2002; 17(1): 53-56
Printed March 1, 2002
Copyright © The Korean Mathematical Society.
Chong-Man Cho
Hanyang University
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.
Keywords: compact operator, cotype $q$, $\ell_p$-sum, Rademacher functions
MSC numbers: 46B28, 46B20
2004; 19(4): 715-720
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