Banach Journal of Mathematical Analysis

Algebraically paranormal operators on Banach spaces

Pietro Aiena

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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.

Article information

Source
Banach J. Math. Anal., Volume 7, Number 2 (2013), 136 -145 .

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1363784227

Digital Object Identifier
doi:10.15352/bjma/1363784227

Mathematical Reviews number (MathSciNet)
MR3039943

Zentralblatt MATH identifier
1291.47015

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

Keywords
paranormal operator polaroid type operator Weyl type theorems

Citation

Aiena , Pietro. Algebraically paranormal operators on Banach spaces. Banach J. Math. Anal. 7 (2013), no. 2, 136 --145. doi:10.15352/bjma/1363784227. https://projecteuclid.org/euclid.bjma/1363784227


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