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2013 Algebraically paranormal operators on Banach spaces
Pietro Aiena
Banach J. Math. Anal. 7(2): 136-145 (2013). DOI: 10.15352/bjma/1363784227

Abstract

In this paper we show that a bounded linear operator on a Banach space $X$ is polaroid if and only if $p(T)$ is polaroid for some polynomial $p$. Consequently, algebraically paranormal operators defined on Banach spaces are hereditarily polaroid. Weyl type theorems are also established for perturbations $f(T+K)$, where $T$ is algebraically paranormal, $K$ is algebraic and commutes with $T$, and $f$ is an analytic function, defined on an open neighborhood of the spectrum of $T+K$, such that $f$ is nonconstant on each of the components of its domain. These results subsume recent results in this area.

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Pietro Aiena . "Algebraically paranormal operators on Banach spaces." Banach J. Math. Anal. 7 (2) 136 - 145, 2013. https://doi.org/10.15352/bjma/1363784227

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1291.47015
MathSciNet: MR3039943
Digital Object Identifier: 10.15352/bjma/1363784227

Subjects:
Primary: 47A10
Secondary: 47A11 , 47A53 , 47A55

Keywords: paranormal operator , polaroid type operator , Weyl type theorems

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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