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Uniqueness of topology for semisimple \(LFQ\)-algebras. (English) Zbl 0784.46031

T. J. Ransford has given a short proof of Barry Johnson’s famous result establishing uniqueness of the norm topology on semisimple Banach algebras. Ransford’s proof uses properties of the spectral radius and owes some of its ideas to B. Aupetit. The present paper extends the Ransford techniques to certain classes of semisimple locally multiplicitively convex algebras. Thus, to exemplify, the uniqueness of (the relevant) complete topology is established for algebras of holomorphic functions on compact Stein sets in complex second countable manifolds.

MSC:

46H40 Automatic continuity
46H05 General theory of topological algebras
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
32A38 Algebras of holomorphic functions of several complex variables
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