Perturbation theory for quasinilpotents in Banach algebras

Xin Wang; Peng Cao

doi:10.3390/math8071163

Perturbation theory for quasinilpotents in Banach algebras

Xin Wang, Peng Cao^*

^*Corresponding author for this work

School of Mathematics and Statistics

Jianghan University

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then qⁿ = 0. Applications to C* algebras are given.

Original language	English
Article number	1163
Journal	Mathematics
Volume	8
Issue number	7
DOIs	https://doi.org/10.3390/math8071163
Publication status	Published - Jul 2020

Keywords

Finite spectrum
Perturbation theory
Quasinilpotent elements
Socle

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10.3390/math8071163

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Wang, X., & Cao, P. (2020). Perturbation theory for quasinilpotents in Banach algebras. Mathematics, 8(7), Article 1163. https://doi.org/10.3390/math8071163

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abstract = "In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then qn = 0. Applications to C* algebras are given.",

keywords = "Finite spectrum, Perturbation theory, Quasinilpotent elements, Socle",

author = "Xin Wang and Peng Cao",

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AU - Cao, Peng

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AB - In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then qn = 0. Applications to C* algebras are given.

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KW - Perturbation theory

KW - Quasinilpotent elements

KW - Socle

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Perturbation theory for quasinilpotents in Banach algebras

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