Rank, trace and determinant in Banach algebras: Generalized Frobenius and Sylvester theorems

Gareth Braatvedt; Rudolf Brits; Francois Schulz

doi:10.4064/sm8157-12-2015

Rank, trace and determinant in Banach algebras: Generalized Frobenius and Sylvester theorems

Gareth Braatvedt
, Rudolf Brits
, Francois Schulz

Mathematics and Applied Mathematics

University of Johannesburg

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

5 Citations (Scopus)

Abstract

As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

Original language	English
Pages (from-to)	173-180
Number of pages	8
Journal	Studia Mathematica
Volume	229
Issue number	2
DOIs	https://doi.org/10.4064/sm8157-12-2015
Publication status	Published - 2015

Keywords

Banach algebra
Rank
Socle
Spectrum

ASJC Scopus subject areas

General Mathematics

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10.4064/sm8157-12-2015

Cite this

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title = "Rank, trace and determinant in Banach algebras: Generalized Frobenius and Sylvester theorems",

abstract = "As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.",

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author = "Gareth Braatvedt and Rudolf Brits and Francois Schulz",

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year = "2015",

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T2 - Generalized Frobenius and Sylvester theorems

AU - Braatvedt, Gareth

AU - Brits, Rudolf

AU - Schulz, Francois

PY - 2015

Y1 - 2015

N2 - As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

AB - As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

KW - Banach algebra

KW - Rank

KW - Socle

KW - Spectrum

UR - https://www.scopus.com/pages/publications/84953873826

U2 - 10.4064/sm8157-12-2015

DO - 10.4064/sm8157-12-2015

M3 - Article

AN - SCOPUS:84953873826

SN - 0039-3223

VL - 229

SP - 173

EP - 180

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -

Rank, trace and determinant in Banach algebras: Generalized Frobenius and Sylvester theorems

Abstract

Keywords

ASJC Scopus subject areas

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