Illinois Journal of Mathematics

The structure of the set of idempotents in a Banach algebra

J. P. Holmes

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Abstract

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.

Article information

Source
Illinois J. Math., Volume 36, Issue 1 (1992), 102-115.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255987609

Digital Object Identifier
doi:10.1215/ijm/1255987609

Mathematical Reviews number (MathSciNet)
MR1133772

Zentralblatt MATH identifier
0766.46035

Subjects
Primary: 46H20: Structure, classification of topological algebras
Secondary: 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05]

Citation

Holmes, J. P. The structure of the set of idempotents in a Banach algebra. Illinois J. Math. 36 (1992), no. 1, 102--115. doi:10.1215/ijm/1255987609. https://projecteuclid.org/euclid.ijm/1255987609


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