Commutativity via spectra of exponentials

Rudi Brits; Francois Schulz; Cheick Touré

doi:10.4153/S0008439521000886

Commutativity via spectra of exponentials

Rudi Brits, Francois Schulz, Cheick Touré

Mathematics and Applied Mathematics

University of Johannesburg

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

1 Citation (Scopus)

Abstract

Let A be a semisimple, unital and complex Banach algebra. It is well-known, and easy to prove that A is commutative if and only exey = ex+y for all x,y ϵ A. Elaborating on the spectral theory of commutativity developed by Aupetit, Zemánek, and Zemánek and Pták, we derive, in this paper, commutativity results via a spectral comparison of exey and ex+y.

Original language	English
Journal	Canadian Mathematical Bulletin
DOIs	https://doi.org/10.4153/S0008439521000886
Publication status	Accepted/In press - 2021

Keywords

Banach algebra
Commutativity
Exponential function
Spectrum

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4153/S0008439521000886

Cite this

@article{ee682da1aae641dd910286817b76400f,

title = "Commutativity via spectra of exponentials",

abstract = "Let A be a semisimple, unital and complex Banach algebra. It is well-known, and easy to prove that A is commutative if and only exey = ex+y for all x,y ϵ A. Elaborating on the spectral theory of commutativity developed by Aupetit, Zem{\'a}nek, and Zem{\'a}nek and Pt{\'a}k, we derive, in this paper, commutativity results via a spectral comparison of exey and ex+y.",

keywords = "Banach algebra, Commutativity, Exponential function, Spectrum",

author = "Rudi Brits and Francois Schulz and Cheick Tour{\'e}",

note = "Publisher Copyright: {\textcopyright} CanadianMathematical Society 2021.",

year = "2021",

doi = "10.4153/S0008439521000886",

language = "English",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

}

TY - JOUR

T1 - Commutativity via spectra of exponentials

AU - Brits, Rudi

AU - Schulz, Francois

AU - Touré, Cheick

PY - 2021

Y1 - 2021

N2 - Let A be a semisimple, unital and complex Banach algebra. It is well-known, and easy to prove that A is commutative if and only exey = ex+y for all x,y ϵ A. Elaborating on the spectral theory of commutativity developed by Aupetit, Zemánek, and Zemánek and Pták, we derive, in this paper, commutativity results via a spectral comparison of exey and ex+y.

AB - Let A be a semisimple, unital and complex Banach algebra. It is well-known, and easy to prove that A is commutative if and only exey = ex+y for all x,y ϵ A. Elaborating on the spectral theory of commutativity developed by Aupetit, Zemánek, and Zemánek and Pták, we derive, in this paper, commutativity results via a spectral comparison of exey and ex+y.

KW - Banach algebra

KW - Commutativity

KW - Exponential function

KW - Spectrum

UR - http://www.scopus.com/inward/record.url?scp=85119176925&partnerID=8YFLogxK

U2 - 10.4153/S0008439521000886

DO - 10.4153/S0008439521000886

M3 - Article

AN - SCOPUS:85119176925

SN - 0008-4395

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

ER -

Commutativity via spectra of exponentials

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this