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.
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