4 papers
Equivalency of the Corona problem and Gleason problem in the theory of SCV
S. R. Patel
We establish an equivalency of the Corona problem (1962) and Gleason problem (1964) in the theory of several complex variables. As an application, we give an affirmative solution o…
On affirmative solution to Michael's acclaimed problem in the theory of Fréchet algebras, with applications to automatic continuity theory
S. R. Patel
In 1952, Michael posed a question about the functional continuity of commutative Frechet algebras in his memoir, known as Michael problem in the literature. We settle this in the a…
On Singer-Wermer conjecture in Frechet algebras
S. R. Patel
We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example…
On discontinuity of derivations, inducing non-unique complete metric topologies
S. R. Patel
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…