On the multiplier algebra of fréchet algebras

Abstract

Let A be a Fréchet algebra and let M(A) denote the algebra of all multipliers of A. In this paper, we show that if A has a bounded approximate identity, then M(A) is a Fréchet algebra with respect to the strict topology. Under this topology, we then study the spectrum of M(A) and provide some examples in this field. Finally, we introduce and study the notion of ϕ-multiplier amenability of A, where ϕ is a complex-valued homomorphism on A. © 2019, Politechnica University of Bucharest. All rights reserved.