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 |
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Pages (from-to) | 2415-2422 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 124 |
Issue number | 8 |
DOIs | |
State | Published - 1996 |
Keywords
- Banach algebra
- C*-algebra
- Invertible elements
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics