Polaroid operators,SVEP and perturbed Browder,Weyl theorems |
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Authors: | B P Duggal |
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Institution: | (1) 8 Redwood Grove, Northfield Avenue Ealing, W5 4SZ London, UK |
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Abstract: | A Banach space operatorT ɛB(X) is polaroid,T ɛP, if the isolated points of the spectrum ofT are poles of the resolvent ofT. LetPS denote the class of operators inP which have have SVEP, the single-valued extension property. It is proved that ifT is polynomiallyPS andA ɛB(X) is an algebraic operator which commutes withT, thenf(T+A) satisfies Weyl’s theorem andf(T
*+A
*) satisfiesa-Weyl’s theorem for everyf which is holomorphic on a neighbourhood of σ(T+A). |
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Keywords: | AMS(MOS) subject classification (2000)" target="_blank">AMS(MOS) subject classification (2000) Primary 47B47 47A10 47A11 |
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