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Pietsch integral operators defined on injective tensor products of spaces and applications

Published online by Cambridge University Press:  18 May 2009

Dumitru Popa
Dumitru Popa
Affiliation:
Department of Mathematics, University of Constanta, 8700 Constanta, Romania
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Abstract

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For X and Y Banach spaces, let X⊗εY, be the injective tensor product. If Z is also a Banach space and U ∊ L(X⊗εY,Z) we consider the operator

We prove that if U ∊ PI(X⊗εY, Z), then U# ∊ I(X, PI(Y,Z)). This result is then applied in the case of operators defined on the space of all X-valued continuous functions on the compact Hausdorff space T. We obtain also an affirmative answer to a problem of J. Diestel and J. J. Uhl about the RNP property for the space of all nuclear operators; namely if X* and Y have the RNP and Y can be complemented in its bidual, then N(X, Y) has the RNP.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 2 , May 1997 , pp. 227 - 230
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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