Invariant subspaces of operators quasi-similar to L-weakly and M-weaklycompact operators | Zendy

Erdal Bayram | Zendy

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Invariant subspaces of operators quasi-similar to L-weakly and M-weaklycompact operators

Author(s) -

Erdal Bayram

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1611-70

Subject(s) - mathematics , invariant subspace problem , compact operator , invariant subspace , finite rank operator , centralizer and normalizer , linear subspace , reflexive operator algebra , compact space , pure mathematics , banach space , bounded function , strictly singular operator , approximation property , operator (biology) , invariant (physics) , bounded operator , operator norm , discrete mathematics , quasinormal operator , operator theory , operator space , mathematical analysis , mathematical physics , computer science , programming language , extension (predicate logic) , repressor , chemistry , biochemistry , transcription factor , gene

Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.

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