Idempotents in an ultrametric Banach algebra

Idempotents in an ultrametric Banach algebra

Abstract Let IK be a complete ultrametric field and let A be a unital commutative ultrametric Banach IK-algebra. Suppose that the multiplicative spectrum admits a partition in two open closed subsets. Then there exist unique idempotents u, v ϵ A such that ϕ (u) = 1, ϕ (v)...

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Autor principal: Escassut,Alain
Lenguaje:English
Publicado: Universidad de La Frontera. Departamento de Matemática y Estadística. 2021
Materias:
ultrametric Banach algebras
multiplicative semi-norms
idempotents
affinoid algebras.
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100161
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spelling oai:scielo:S0719-064620210001001612021-05-11Idempotents in an ultrametric Banach algebraEscassut,Alain ultrametric Banach algebras multiplicative semi-norms idempotents affinoid algebras. Abstract Let IK be a complete ultrametric field and let A be a unital commutative ultrametric Banach IK-algebra. Suppose that the multiplicative spectrum admits a partition in two open closed subsets. Then there exist unique idempotents u, v &#1013; A such that &#981; (u) = 1, &#981; (v) = 0 &#8704; &#981; &#1013; U, &#981; (u) = 0 &#981; (v) = 1 &#8704; &#981; &#1013; V . Suppose that IK is algebraically closed. If an element x &#1013; A has an empty annulus r < |&#958; &#8722; a| < s in its spectrum sp(x), then there exist unique idempotents u, v such that &#981; (u) = 1; &#981; (v) = 0 whenever &#981; (x &#8722; a) &#8804; r and &#981; (u) = 0; &#981; (v) = 1 whenever &#981; (x &#8722; a) &#8805; s.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.23 n.1 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100161en10.4067/S0719-06462021000100161
institution Scielo Chile
collection Scielo Chile
language English
topic ultrametric Banach algebras
multiplicative semi-norms
idempotents
affinoid algebras.
spellingShingle ultrametric Banach algebras
multiplicative semi-norms
idempotents
affinoid algebras.
Escassut,Alain
Idempotents in an ultrametric Banach algebra
description Abstract Let IK be a complete ultrametric field and let A be a unital commutative ultrametric Banach IK-algebra. Suppose that the multiplicative spectrum admits a partition in two open closed subsets. Then there exist unique idempotents u, v &#1013; A such that &#981; (u) = 1, &#981; (v) = 0 &#8704; &#981; &#1013; U, &#981; (u) = 0 &#981; (v) = 1 &#8704; &#981; &#1013; V . Suppose that IK is algebraically closed. If an element x &#1013; A has an empty annulus r < |&#958; &#8722; a| < s in its spectrum sp(x), then there exist unique idempotents u, v such that &#981; (u) = 1; &#981; (v) = 0 whenever &#981; (x &#8722; a) &#8804; r and &#981; (u) = 0; &#981; (v) = 1 whenever &#981; (x &#8722; a) &#8805; s.
author Escassut,Alain
author_facet Escassut,Alain
author_sort Escassut,Alain
title Idempotents in an ultrametric Banach algebra
title_short Idempotents in an ultrametric Banach algebra
title_full Idempotents in an ultrametric Banach algebra
title_fullStr Idempotents in an ultrametric Banach algebra
title_full_unstemmed Idempotents in an ultrametric Banach algebra
title_sort idempotents in an ultrametric banach algebra
publisher Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate 2021
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100161
work_keys_str_mv AT escassutalain idempotentsinanultrametricbanachalgebra
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