Semisimple Segal Fréchet algebras

Abstract

In this paper, we recall the concept of Segal Fréchet algebra in a Fréchet algebra (A, pℓ) and show that in some cases, every continuous linear left multiplier on (A, p ℓ) is a continuous linear left multiplier of any Segal Fréchet algebra (B, q m) in (A, p ℓ). As the main result, we prove that if A is a commutative Fréchet Q-algebra with an approximate identity, A is semisimple if and only if B is semisimple. © 2015 Akadémiai Kiadó, Budapest, Hungary.