arXiv 2002.063652020-02-15math.FA

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

S. R. Patel

备注：: 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

英文摘要：

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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