Some invariant subspaces for w-hyponormal operators

In this paper, we prove that if is w-hyponormal, then the quasinilpotent part of T is given by for all sufficiently large integers p, where . We prove that if T is w-hyponormal and the spectrum is finite, then T is algebraic. In addition, we prove that if is w-hyponormal and has decomposition proper...

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Published in:Linear & multilinear algebra Vol. 67; no. 7; pp. 1460 - 1470
Main Author: Rashid, M. H. M.
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.07.2019
Taylor & Francis Ltd
Subjects:
Bishop's property
decomposable operator
decomposition property
Integers
invariant property (I)
Invariants
local spectrum
Operators
Subspaces
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary:In this paper, we prove that if is w-hyponormal, then the quasinilpotent part of T is given by for all sufficiently large integers p, where . We prove that if T is w-hyponormal and the spectrum is finite, then T is algebraic. In addition, we prove that if is w-hyponormal and has decomposition property , then T has a non-trivial invariant closed linear subspace. Also, we obtain that such an operator with rich spectrum has a nontrivial invariant subspace. Moreover, we consider invariant and hyperinvariant subspaces for w-hyponormal operators.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2018.1455803