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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Locally finite-dimensional sets of operators


Author: Leonya Livshits
Journal: Proc. Amer. Math. Soc. 119 (1993), 165-169
MSC: Primary 47D99; Secondary 47A99, 47D15
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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1159175-8
PII: S 0002-9939(1993)1159175-8
Article copyright: © Copyright 1993 American Mathematical Society