Translator Disclaimer
Spring 1992 The structure of the set of idempotents in a Banach algebra
J. P. Holmes
Author Affiliations +
Illinois J. Math. 36(1): 102-115 (Spring 1992). DOI: 10.1215/ijm/1255987609


We study here the algebraic, geometric, and analytic structure of the set of idempotent elements in a real or complex Banach algebra. A neighborhood of each idempotent in the set of idempotents forms the set of idempotents in a Rees product subsemigroup of the Banach algebra. Each nontrivial connected component of the set of idempotents is shown to be a generalized saddle, a type of analytic manifold. Each component is also shown to be the quotient of a (possibly infinite dimensional) Lie group by a Lie subgroup.


Download Citation

J. P. Holmes. "The structure of the set of idempotents in a Banach algebra." Illinois J. Math. 36 (1) 102 - 115, Spring 1992.


Published: Spring 1992
First available in Project Euclid: 19 October 2009

MathSciNet: MR1133772
zbMATH: 0766.46035
Digital Object Identifier: 10.1215/ijm/1255987609

Primary: 46H20
Secondary: 22E65

Rights: Copyright © 1992 University of Illinois at Urbana-Champaign


Vol.36 • No. 1 • Spring 1992
Back to Top