• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.271-279
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• 2009

In this paper, we prove that asymptotically quasisimilar sub-decomposable operators have equal spectra and quasisimilar decomposable operators have equal spectra. Moreover, every subscalar operator is admissible.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.653-659
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• 2005

In this paper it is proved that quasisimilar n-tuples of tensor products of injective p-quasihyponormal operators have the same spectra, essential spectra and indices, respectively. And it is also proved that a Weyl n-tuple of tensor products of injective p-quasihyponormal operators can be perturbed by an n-tuple of compact operators to an invertible n-tuple.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.185-189
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• 2013

In this note we study a class of invertible weighted bilateral shifts on Hilbert space introduced by Haskell Rosenthal recently. We show that every Rosenthal shift is unitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivial hyperinvariant subspace.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.785-794
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• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(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.