Inverse closedness of C*-algebras in Banach algebras

Authors
Goldstein, D
Citation
D. Goldstein, Inverse closedness of C*-algebras in Banach algebras, INTEG EQ OP, 33(2), 1999, pp. 172-174
Citations number
3
Categorie Soggetti
Mathematics
Journal title
INTEGRAL EQUATIONS AND OPERATOR THEORY
ISSN journal
0378620X → ACNP
Volume
33
Issue
2
Year of publication
1999
Pages
172 - 174
Database
ISI
SICI code
0378-620X(199902)33:2<172:ICOCIB>2.0.ZU;2-W
Abstract
Let A denote a unital Banach algebra, and let B denote a C*-algebra which i s contained as a unital subalgebra in A. We prove that B is inverse closed in A if the norms of A and B coincide. This generalizes well known result a bout inverse closedness of C*-subalgebras in C*-algebras.