TY - JOUR
TI - On discontinuity of derivations, inducing inequivalent complete metric topologies
PY - 2024/05/31
Y2 - 2024/10/15
JF - Extracta Mathematicae
JA - Extr. Math.
VL - 39
IS - 1
SE - Functional Analysis and Operator Theory
DO - 10.17398/2605-5686.39.1.1
UR - https://doi.org/10.17398/2605-5686.39.1.1
SP - 1--17
AB - 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.
ER -