International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1980 / Article

Open Access

Volume 3 |Article ID 930656 | https://doi.org/10.1155/S0161171280000324

J. M. Baker, "Operator representation of weakly Cauchy sequences in projective tensor products of Banach spaces", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 930656, 10 pages, 1980. https://doi.org/10.1155/S0161171280000324

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

Received22 Aug 1979

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.

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.


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