On discontinuity of derivations, inducing inequivalent complete metric topologies

• S.R. Patel ^[1]
  1. [1] Department of Mathematics, C.U. Shah University Wadhwan City, Gujarat, INDIA
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 39, Nº 1, 2024, págs. 1-17
• Idioma: inglés
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• Resumen

  • We give an elementary method for constructing commutative Fréchet algebras with non-unique Fréchet algebra topology. 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 (1974) for Fréchet algebras. We also obtain the uniqueness of the Fréchet algebra topology of certain Fréchet algebras with finite dimensional radicals.