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Some properties of the projective tensor product UX derived from those of U and X

Published online by Cambridge University Press:  17 April 2009

Patrick N. Dowling
Patrick N. Dowling
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, United States of America, e-mail: dowlinpn@muohio.edu
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Let X be a real or complex Banach space and let U be a Banach space with an unconditional basis. We show that the projective tensor product of U and X, UX, has the complete continuity property (respectively, the analytic complete continuity property) whenever U and X have the complete continuity property (respectively, the analytic complete continuity property). More general versions of these results are also obtained. Moreover, the techniques applied here to the projective tensor product, can also be used to establish some Banach space properties of the Fremlin projective tensor product.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 37 - 45
Copyright
Copyright © Australian Mathematical Society 2006

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