hal.structure.identifier	Laboratoire Bordelais d'Analyse et Géométrie [LaBAG]
dc.contributor.author	GIOL, Julien
dc.date.issued	2007
dc.description.abstractEn	If p,q are idempotents in a Banach algebra A and if p+q-1 is invertible, then the Kovarik formula provides an idempotent k(p,q) such that pA=k(p,q)A and Aq=Ak(p,q). We study the existence of such an element in a more general situation. We first show that p+q-1 is invertible if and only if k(p,q) and k(q,p) both exist. Then we deduce a local parametrization of the set of idempotents from this equivalence. Finally, we consider a polynomial parametrization first introduced by Holmes and we answer a question raised at the end of his paper.
dc.language.iso	en
dc.title.en	From a formula of Kovarik to the parametrization of idempotents in Banach algebra.
dc.type	Article de revue
dc.subject.hal	Mathématiques [math]/Analyse fonctionnelle [math.FA]
bordeaux.journal	Illinois Journal of Mathematics
bordeaux.page	429-444
bordeaux.volume	51
bordeaux.issue	2
bordeaux.peerReviewed	oui
hal.identifier	hal-00288818
hal.version	1
hal.origin.link	https://hal.archives-ouvertes.fr//hal-00288818v1
bordeaux.COinS	ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Illinois%20Journal%20of%20Mathematics&rft.date=2007&rft.volume=51&rft.issue=2&rft.spage=429-444&rft.epage=429-444&rft.au=GIOL,%20Julien&rft.genre=article

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From a formula of Kovarik to the parametrization of idempotents in Banach algebra.