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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the dual of a certain operator ideal


Author: Gerhard Racher
Journal: Proc. Amer. Math. Soc. 82 (1981), 36-38
MSC: Primary 47D35; Secondary 46M35
DOI: https://doi.org/10.1090/S0002-9939-1981-0603597-X
MathSciNet review: 603597
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Abstract: For complex Banach spaces $ E$ and $ F$ and a real number $ 1 < p < \infty $ let $ {S^p}(E,F)$ denote the operator ideal obtained by complex interpolation between the nuclear and the compact operators. If $ E$ and $ F$ are reflexive and one of them has the approximation property the dual of $ {S^p}(E,F)$ is shown to be $ {S^{p'}}(E',F')$, $ p'$ conjugate to $ p$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603597-X
Keywords: Reflexivity, operator ideals, nuclear and compact operators, complex interpolation
Article copyright: © Copyright 1981 American Mathematical Society