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Proceedings of the American Mathematical Society

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

 

 

Reflexivity of operator spaces


Author: J. M. Baker
Journal: Proc. Amer. Math. Soc. 85 (1982), 366-368
MSC: Primary 47D15; Secondary 46A32, 46B10
MathSciNet review: 656104
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Abstract: For reflexive Banach spaces $ E$ and $ F$ (with $ E$ or $ F$ having the approximation property), the space of opeartors from $ E$ into $ F$ (the inductive tensor product of $ {E^ * }$ with $ F$) is reflexive if and only if the operator space coincides with the inductive tensor product of $ {E^ * }$ with $ F$. Consequently, $ E$ must be finite-dimensional if either the projective tensor product of $ E$ with $ {E^ * }$ is reflexive, or the inductive tensor product of $ E$ with $ {E^ * }$ is reflexive and $ E$ has the approximation property.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0656104-0
Article copyright: © Copyright 1982 American Mathematical Society