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Proceedings of the American Mathematical Society

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

 

 

On algebras generated by invertible operators


Author: Avraham Feintuch
Journal: Proc. Amer. Math. Soc. 63 (1977), 66-68
MSC: Primary 47C05; Secondary 47A65
MathSciNet review: 0435929
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Abstract: Let T be an invertible operator such that the compact operators in $ R(T)$ are weakly dense in it. Then $ {T^{ - 1}} \in R(T)$. In particular, if T is an essentially unitary $ {C_0}$ operator, $ {T^{ - 1}} \in R(T)$.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0435929-9
Keywords: Invertible operators, weakly closed algebras, compact operators, invariant subspace
Article copyright: © Copyright 1977 American Mathematical Society