On discontinuity of derivations, inducing non-unique complete metric topologies

2020/02/15 by S. R. Patel, Patel, S. R.
Mathematics · #46H40 #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Primary 46J05 #Secondary 13F25

paper · pdf · doi:10.48550/arxiv.2002.06365

openalex publication_date 2020/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a simple method for constructing commutative Frechet algebras which admit two inequivalent Frechet algebra topologies. The result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined among other useful applications. We give an affirmative answer to a question of Loy from 1974. We also obtain the uniqueness of the Frechet algebra topology of certain Frechet algebras with finite dimensional radicals.

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