Fragoulopoulou, Maria Uniqueness of topology for semisimple \(LFQ\)-algebras. (English) Zbl 0784.46031 Proc. Am. Math. Soc. 117, No. 4, 963-969 (1993). 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. Reviewer: K.B.Laursen (København) Cited in 2 ReviewsCited in 5 Documents 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 Keywords:closed graph pair; barrelled Ptak \(Q\)-algebra; uniqueness of the norm topology on semisimple Banach algebras; semisimple locally multiplicitively convex algebras; algebras of holomorphic functions on compact Stein sets in complex second countable manifolds PDFBibTeX XMLCite \textit{M. Fragoulopoulou}, Proc. Am. Math. Soc. 117, No. 4, 963--969 (1993; Zbl 0784.46031) Full Text: DOI