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

 

Invariant subspace of strictly singular operators


Author: Ji Shou Ruan
Journal: Proc. Amer. Math. Soc. 108 (1990), 931-936
MSC: Primary 47A15; Secondary 47H09
Remark: Proc. Amer. Math. Soc. 112, no. 2 (1991), p. 601.
MathSciNet review: 1002160
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Abstract: In this paper, we show that strictly singular operators are condensing maps. Moreover, we obtain a new result that every bounded linear operator $ T$ on a Banach space that commutes with a nonzero strictly singular operator $ S$ has a non-trivial invariant closed subspace.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1002160-4
PII: S 0002-9939(1990)1002160-4
Keywords: Invariant subspace, strictly singular operator, fixed point theorem, condensing map, measure of noncompactness, partition of unity, paracompact, Zorn's Lemma, Tychonoff's Theorem
Article copyright: © Copyright 1990 American Mathematical Society