Geodesic
On the Invariance of the Spectrum in Locally m-Convex Algebras
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 658-664

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider two closely related problems concerning a complete locally m-convex (LMC) algebra A with identity. Let a be a fixed element of A, and let P(a) be the smallest closed subalgebra containing a and 1. If B is any subalgebra containing a and 1, we let σ(a; B) denote the spectrum of a as an element of B. (I) Describe the set σ(a; P(a)) in terms of σ(a; A). (II) Give necessary and sufficient conditions in order that σ (a; B) = σ(a; A) for every closed subalgebra B of A which contains a and 1. 
Brooks, R. M. On the Invariance of the Spectrum in Locally m-Convex Algebras. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 658-664. doi: 10.4153/CJM-1968-063-9
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