Showing papers by "Muneo Chō published in 2011"
TL;DR: In this article, the authors characterize perturbations of dAB by quasinilpotent and algebraic operators A, B ∈ B(H) for any function f which is analytic on a neighbourhood of σ(dAB).
Abstract: A Banach space operator T ∈ B(X ) is hereditarily polaroid, T ∈ (HP), if the isolated points of the spectrum of every part Tp of the operator are poles of the resolvent of Tp; T is hereditarly normaloid, T ∈ (HN ), if every part Tp of T is normaloid. Let (HNP) denote the class of operators T ∈ B(X ) such that T ∈ (HP)∩ (HN ). (HNP) operators such that the Berberian–Quigley extension T◦ of T is also in (HNP) satisfy Bishop’s property (β). Given Hilbert space operators A, B∗ ∈ B(H), let dAB ∈ B(B(H)) stands for either of the elementary operators δAB(X) = AX−XB and 4AB(X) = AXB−X. If A, B∗ ∈ (HP) satisfy property (β), and the eigenspaces corresponding to distinct eigenvalues of A (resp., B∗) are orthogonal, then f(dAB) satisfies Weyl’s theorem and f(dAB) ∗ satisfies a-Weyl’s theorem for every function f which is analytic on a neighbourhood of σ(dAB). Finally, we characterize perturbations of dAB by quasinilpotent and algebraic operators A, B ∈ B(H).
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