Reflexivity of operator spaces

Baker, J. M.

doi:10.1090/S0002-9939-1982-0656104-0

Reflexivity of operator spaces
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by J. M. Baker

Proc. Amer. Math. Soc. 85 (1982), 366-368

DOI: https://doi.org/10.1090/S0002-9939-1982-0656104-0

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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.

References

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