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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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society Vol. 99; no. 2; pp. 274 - 283
Main Authors: ASSADI, AMANOLLAH, FARZANEH, MOHAMAD ALI, MOHAMMADINEJAD, HAJI MOHAMMAD
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.04.2019
Subjects:
Banach spaces
Decomposition
Invariants
Linear operators
Subspaces
secondary 47A55
subspace
defect
almost-invariant subspace
primary 47A15
finite-rank operator
half-space
ISSN:0004-9727, 1755-1633
Online Access:Get full text
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Summary: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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ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972718001363