On invertibility symbols in Banach algebras

Naum Krupnik; Steffen Roch

doi:10.1016/0024-3795(94)00214-2

On invertibility symbols in Banach algebras

Naum Krupnik, Steffen Roch

Department of Mathematics

Leipzig University

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

1 Scopus citations

Abstract

It is shown that, if the algebra Script A sign^{n × n} of all n × n matrices with entries belonging to a Banach algebra Script A sign possesses an invertibility symbol of order mn, then the algebra Script A sign possesses an invertibility symbol of order m. The proof is based on converse Amitsur-Levitzky theorems.

Original language	English
Pages (from-to)	77-81
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	245
DOIs	https://doi.org/10.1016/0024-3795(94)00214-2
State	Published - 15 Sep 1996

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AB - It is shown that, if the algebra Script A signn × n of all n × n matrices with entries belonging to a Banach algebra Script A sign possesses an invertibility symbol of order mn, then the algebra Script A sign possesses an invertibility symbol of order m. The proof is based on converse Amitsur-Levitzky theorems.

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On invertibility symbols in Banach algebras

Abstract

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