AUTOMATIC CONTINUITY OF SURJECTIVE ALMOST DERIVATIONS ON FRECHET Q-ALGEBRAS

Document Type : Original Article

Authors
C. GANESA MOORTHY
GURUSAMY SIVA
Department of Mathematics, Alagappa University, Karaikudi630 003, India.
10.22034/maco.3.1.5
Abstract
In 1971 R. L. Carpenter proved that every derivation T on a semisimple commutative Frechet algebra Λ with identity is continuous. By relaxing the commutativity assumption on Λ and adding the surjectivity assumption on T, we derive a corresponding continuity result, for a new concept of almost derivations on Frechet algebras in this article. Also, it is further proved that every surjective almost derivation T on non commutative semisimple Frechet Q-algebras Λ with an additional condition on Λ, is continuous. Moreover, an example is provided to illustrate our main result.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 3, Issue 1
June 2022
Pages 43-48