Duggal, B. P. Polaroid operators, SVEP and perturbed Browder, Weyl theorems. (English) Zbl 1196.47030 Rend. Circ. Mat. Palermo (2) 56, No. 3, 317-330 (2007). Summary: A Banach space operator \(T\in B(\mathcal X)\) is polaroid, \(T\in\mathcal P\), if the isolated points of the spectrum of \(T\) are poles of the resolvent of \(T\). Let \(\mathcal{PS}\) denote the class of operators in \(\mathcal P\) which have the single-valued extension property (SVEP). It is proved that, if \(\mathcal T\) is polynomially \(\mathcal{PS}\) and \(A\in B(\mathcal X)\) is an algebraic operator which commutes with \(T\), then \(f(T+A)\) satisfies Weyl’s theorem and \(f(T^*+A^*)\) satisfies \(a\)-Weyl’s theorem for every \(f\) which is holomorphic on a neighbourhood of \(\sigma(T+A)\). Cited in 5 Documents MSC: 47B47 Commutators, derivations, elementary operators, etc. 47A10 Spectrum, resolvent 47A11 Local spectral properties of linear operators Keywords:Banach space; polaroid operator; single-valued extension property; algebraic operator; polynomial operator; orthogonal subspaces; Browder’s theorem; Weyl’s theorem PDFBibTeX XMLCite \textit{B. P. Duggal}, Rend. Circ. Mat. Palermo (2) 56, No. 3, 317--330 (2007; Zbl 1196.47030) Full Text: DOI References: [1] Aiena P.,Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer, 2004. · Zbl 1077.47001 [2] Aiena P.,Classes of operators satisfying a-Weyl’s theorem, Studia Math.,169 (2005), 137–151. · Zbl 1071.47001 [3] Aiena P., Guillen J. R.,Weyl’s theorem for perturbations of paranormal operators, Proc. Amer. Math. Soc.,135 (2007), 2443–2451. · Zbl 1117.47003 [4] Benhida C., Zerouali E. H., Zguitti H.,Spectral properties of upper triangular block operators, Acta Sci. Math. 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