On discontinuity of derivations, inducing inequivalent complete metric topologies

Autores/as

  • S.R. Patel Department of Mathematics, C.U. Shah University Wadhwan City, Gujarat, INDIA

DOI:

https://doi.org/10.17398/2605-5686.39.1.1

Palabras clave:

Fréchet algebra of power series in infinitely many indeterminates, derivation, (in)equivalent Fréchet algebra topologies, Loy’s question

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.

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Referencias

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Publicado

2024-05-31

Número

Sección

Functional Analysis and Operator Theory

Cómo citar

On discontinuity of derivations, inducing inequivalent complete metric topologies. (2024). Extracta Mathematicae, 39(1), 1-17. https://doi.org/10.17398/2605-5686.39.1.1