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: | |
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| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2021
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100161 |
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| Sumario: | 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) = 0 ∀ ϕ ϵ U, ϕ (u) = 0 ϕ (v) = 1 ∀ ϕ ϵ V . Suppose that IK is algebraically closed. If an element x ϵ A has an empty annulus r < |ξ − a| < s in its spectrum sp(x), then there exist unique idempotents u, v such that ϕ (u) = 1; ϕ (v) = 0 whenever ϕ (x − a) ≤ r and ϕ (u) = 0; ϕ (v) = 1 whenever ϕ (x − a) ≥ s. |
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