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ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES

Part of: General theory of linear operators

Published online by Cambridge University Press:  04 January 2019

AMANOLLAH ASSADI ,
MOHAMAD ALI FARZANEH  and
HAJI MOHAMMAD MOHAMMADINEJAD
AMANOLLAH ASSADI
Affiliation:
Department of Mathematical and Statistical Sciences, University of Birjand, PO Box 97175/615, Birjand, Iran email [email protected]
MOHAMAD ALI FARZANEH*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Birjand, PO Box 97175/615, Birjand, Iran email [email protected]
HAJI MOHAMMAD MOHAMMADINEJAD
Affiliation:
Department of Mathematical and Statistical Sciences, University of Birjand, PO Box 97175/615, Birjand, Iran email [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

subspacealmost-invariant subspacehalf-spacefinite-rank operatordefect

MSC classification

Primary: 47A15: Invariant subspaces
Secondary: 47A55: Perturbation theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 274 - 283
Copyright
© 2019 Australian Mathematical Publishing Association Inc. 

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