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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Vydáno v:Bulletin of the Australian Mathematical Society Ročník 99; číslo 2; s. 274 - 283
Hlavní autoři: ASSADI, AMANOLLAH, FARZANEH, MOHAMAD ALI, MOHAMMADINEJAD, HAJI MOHAMMAD
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.04.2019
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972718001363