Reflexivity of $L(E, F)$
Author:
William H. Ruckle
Journal:
Proc. Amer. Math. Soc. 34 (1972), 171-174
MSC:
Primary 46B10; Secondary 47A99
DOI:
https://doi.org/10.1090/S0002-9939-1972-0291777-X
MathSciNet review:
0291777
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Abstract | References | Similar Articles | Additional Information
Abstract: Let E and F be two Banach spaces both having the approximation property. The space $L(E,F)$ is reflexive if and only if (a) both E and F are reflexive, (b) every continuous linear operator from E into F is compact. Thus $L({l^p},{l^q})$ is reflexive for $1 < q < p < \infty$.
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539 H. R. Pitt, A note on bilinear forms, J. London Math. Soc. 11 (1936), 174-180.
- Haskell P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from $L^{p}\,(\mu )$ to $L^{r}\,(\nu )$, J. Functional Analysis 4 (1969), 176–214. MR 0250036, DOI https://doi.org/10.1016/0022-1236%2869%2990011-1
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Keywords:
Reflexivity,
continuous linear operator,
compact linear operator,
integral operator,
nuclear operator
Article copyright:
© Copyright 1972
American Mathematical Society
