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

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

Department of Mathematics, Western Carolina University, Cullowhee 28723, North Carolina, USA

Received 22 August 1979

Copyright © 1980 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.