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 ∈ A such that φ(u) = 1, φ(v) = 0 ∀φ ∈ U, φ(u) = 0 φ(v) =1 ∀φ ∈ V . Suppose that IK is algebraically closed. If an element x ∈ 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.
Origin : Publisher files allowed on an open archive
Licence : CC BY NC - Attribution - NonCommercial
Licence : CC BY NC - Attribution - NonCommercial