International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 445-454
doi:10.1155/S0161171280000324

Operator representation of weakly Cauchy sequences in projective tensor product of Banach spaces

Abstract

It is shown that the above sequences always determine linear transformations and if the sequences are bounded under the least cross norm, that the transformations are continuous. Such operators are characterized to within algebraic isomorphism with the weak-star sequential closure of the tensor product space in its second dual, and consequently certain classes of weakly sequentially complete projective tensor products are exhibited.