Affine mappings of invertible operators

Lawrence A. Harris; Richard V. Kadison

doi:10.1090/S0002-9939-96-03445-4

Affine mappings of invertible operators

Lawrence A. Harris, Richard V. Kadison

Mathematics

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

14 Scopus citations

Abstract

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

Original language	English
Pages (from-to)	2415-2422
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	124
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-96-03445-4
State	Published - 1996

Keywords

Banach algebra
C*-algebra
Invertible elements

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-96-03445-4

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abstract = "The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.",

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AU - Kadison, Richard V.

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AB - The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

KW - Banach algebra

KW - C-algebra

KW - Invertible elements

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

Affine mappings of invertible operators

Abstract

Keywords

ASJC Scopus subject areas

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