Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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LOCAL SPECTRAL THEORY AND QUASINILPOTENT OPERATORS

  • Received : 2022.02.21
  • Accepted : 2022.03.16
  • Published : 2022.05.30
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Abstract

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then XA(F) = XA+R(F) for all subset F ⊆ ℂ and 𝜎loc(A) = 𝜎loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

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References

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