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  • ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES

  • Part of
  • AMANOLLAH ASSADI, MOHAMAD ALI FARZANEH, HAJI MOHAMMAD MOHAMMADINEJAD
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 99 / Issue 2 / April 2019
    Published online by Cambridge University Press:
    04 January 2019, pp. 274-283
    Print publication:
    April 2019
    • Article
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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.