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Proceedings of the American Mathematical Society

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



Most similarity orbits are strongly dense

Authors: D. W. Hadwin, E. A. Nordgren, Heydar Radjavi and Peter Rosenthal
Journal: Proc. Amer. Math. Soc. 76 (1979), 250-252
MSC: Primary 47A65; Secondary 47A15
MathSciNet review: 537082
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Abstract: It is shown that the strong and weak closures of the similarity orbit of an operator on a Banach space always coincide, and a simple characterization of these closures is given. Whenever an operator is not the sum of a scalar and a finite rank operator, its similarity orbit is strongly dense in the set of all bounded linear operators.

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Keywords: Banach space, operator, similarity orbit, weak and strong operator topologies, finite rank operator
Article copyright: © Copyright 1979 American Mathematical Society