The structure of the set of idempotents in a Banach algebra
Holmes, J. P.
Illinois J. Math., Tome 36 (1992) no. 4, p. 102-115 / Harvested from Project Euclid
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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.
Publié le : 1992-03-15
Classification:  46H20,  22E65 
@article{1255987609,
     author = {Holmes, J. P.},
     title = {The structure of the set of idempotents in a Banach algebra},
     journal = {Illinois J. Math.},
     volume = {36},
     number = {4},
     year = {1992},
     pages = { 102-115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255987609}
}

Holmes, J. P. The structure of the set of idempotents in a Banach algebra. Illinois J. Math., Tome 36 (1992) no. 4, pp.  102-115. http://gdmltest.u-ga.fr/item/1255987609/