Perturbation theory for the socle in Banach algebras

Peng Cao

doi:10.1016/j.jmaa.2018.11.068

Perturbation theory for the socle in Banach algebras

Peng Cao

School of Mathematics and Statistics

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

1 Citation (Scopus)

Abstract

In this paper, we will give a characterization of the socle of a semisimple Banach algebra by perturbation of full spectrum. That is, an element, saying x, lies in the socle if and only if for every element in the Banach algebra, the change under its perturbation (plus x) of full spectrum is finite.

Original language	English
Pages (from-to)	1132-1135
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	472
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.11.068
Publication status	Published - 1 Apr 2019

Keywords

Finite spectrum
Full spectrum
Perturbation theory
Socle

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10.1016/j.jmaa.2018.11.068

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title = "Perturbation theory for the socle in Banach algebras",

abstract = "In this paper, we will give a characterization of the socle of a semisimple Banach algebra by perturbation of full spectrum. That is, an element, saying x, lies in the socle if and only if for every element in the Banach algebra, the change under its perturbation (plus x) of full spectrum is finite.",

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KW - Finite spectrum

KW - Full spectrum

KW - Perturbation theory

KW - Socle

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Perturbation theory for the socle in Banach algebras

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Keywords

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