Unconditionally convergent series of operators on Banach spaces

[摘要] We show that any series Sigma(n), K-n of operators in L(X, Y) that is unconditionally convergent in the weak operator topology and satisfies the condition that Sigma(n is an element of F) K-n is a compact operator for every index set F subset of or equal to N is unconditionally convergent in the uniform operator topology if and only if X*, the dual space of the Banach space X,contains no copy of C-0. (C) 1997 Academic Press.

[发布日期] 1997-03-15