On discontinuity of derivations, inducing non-unique complete metric topologies
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.
Keywords
Cite
@article{arxiv.2002.06365,
title = {On discontinuity of derivations, inducing non-unique complete metric topologies},
author = {S. R. Patel},
journal= {arXiv preprint arXiv:2002.06365},
year = {2020}
}
Comments
Read used "tensor product by rows" method to show that a certain algebra admits two inequivalent topology and showed that Singer-Wermer conjecture fails in the Frechet case. We study discontinuity of derivation/functional in detail. The 2nd paper gives examples with countably many inequivalent topologies; the 2nd example satisfies this conjecture, and admits countably many equivalent topologies