A class of commutative Banach algebras which satisfy a Bochner–Schoenberg–Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Fréchet algebra . Moreover, we verify and generalize some of the main results in the class of Banach algebras, for the Fréchet case. We prove that all Fréchet -algebras and also uniform Fréchet algebras are BSE algebras. Also, we show that is not a Fréchet BSE algebra.
"BSE PROPERTY OF FRÉCHET ALGEBRA." Rocky Mountain J. Math. 53 (5) 1553 - 1570, October 2023. https://doi.org/10.1216/rmj.2023.53.1553