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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Locally finite-dimensional sets of operators
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by Leonya Livshits PDF
Proc. Amer. Math. Soc. 119 (1993), 165-169 Request permission

Abstract:

For any pair of Banach spaces $V$ and $W$ a "global" description is given for the sets $S$ of operators in $B(V,W)$ satisfying the "local" condition that the linear span of the set $\{ T(x)|T \in S\}$ is finite-dimensional for every $x$ in $V$.
References
  • Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. MR 0065561
  • David R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), no. 2, 283–299. MR 935008, DOI 10.2307/2374503
    • L. Livshits, Generalised Schur products for matricies with operator entries, Ph.D. Thesis, Univ. of Toronto, 1991.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 119 (1993), 165-169
  • MSC: Primary 47D99; Secondary 47A99, 47D15
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1159175-8
  • MathSciNet review: 1159175