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Locally finite-dimensional sets of operators


Author: Leonya Livshits
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
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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)\vert T \in S\} $ is finite-dimensional for every $ x$ in $ V$.


References [Enhancements On Off] (What's this?)

  • [1] I. Kaplansky, Infinite abelian groups, Univ. of Michigan Press, Ann Arbor, MI, 1954. MR 0065561 (16:444g)
  • [2] D. R. Larson, Reflexivity, algebraic reflexivity and linear interpolation, Amer. J. Math. 110 (1988), 283-299. MR 935008 (89d:47096)
  • [3] L. Livshits, Generalised Schur products for matricies with operator entries, Ph.D. Thesis, Univ. of Toronto, 1991.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1159175-8
Article copyright: © Copyright 1993 American Mathematical Society

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