ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES
We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace...
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| Published in: | Bulletin of the Australian Mathematical Society Vol. 99; no. 2; pp. 274 - 283 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cambridge, UK
Cambridge University Press
01.04.2019
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| ISSN: | 0004-9727, 1755-1633 |
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| Abstract | We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator. |
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| AbstractList | We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator. |
| Author | FARZANEH, MOHAMAD ALI ASSADI, AMANOLLAH MOHAMMADINEJAD, HAJI MOHAMMAD |
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| Cites_doi | 10.1016/j.jfa.2014.07.007 10.1007/BF02392260 10.1002/mana.19951730107 10.1112/blms/17.4.305 10.1007/s00020-009-1708-8 10.1112/S0024610797005486 10.1016/j.laa.2016.06.025 10.1016/j.jfa.2013.04.002 10.1007/s00020-010-1778-7 10.1016/j.jfa.2012.11.010 |
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| DOI | 10.1017/S0004972718001363 |
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| DocumentTitleAlternate | A. Assadi, M. A. Farzaneh and H. M. Mohammadinejad Operators with several almost-invariant subspaces |
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| Keywords | secondary 47A55 subspace defect almost-invariant subspace primary 47A15 finite-rank operator half-space |
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| Snippet | We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators... |
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| StartPage | 274 |
| SubjectTerms | Banach spaces Decomposition Invariants Linear operators Subspaces |
| Title | ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES |
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