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Proceedings of the American Mathematical Society

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

 

 

Small commutators and invariant subspaces


Author: Hua Xin Lin
Journal: Proc. Amer. Math. Soc. 96 (1986), 443-446
MSC: Primary 47A15; Secondary 47B47
DOI: https://doi.org/10.1090/S0002-9939-1986-0822436-X
MathSciNet review: 822436
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Abstract: Let $ A$ be an operator on a Banach space, and let $ T$ be a nonzero compact (polynomial compact) operator. We prove that if $ TA - AT$ is "small", then $ A$ has a nontrivial (hyper)invariant subspace.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0822436-X
Article copyright: © Copyright 1986 American Mathematical Society