Search

We study solutions and approximate solutions of the multiplicative Sincov equation T (f , h) = T (f , g) T (g , h) for mapping T taking values in a commutative Banach algebra. [ABSTRACT FROM AUTHOR]

Let A be a Banach algebra and let X be a Banach A-bimodule. We consider the Banach algebra ${A\oplus _1 X}$ , where A is a commutative Banach algebra. We investigate the Bochner–Schoenberg–Eberlein (BSE) property and the BSE module property on $A\oplus _1 X$. We show that the module extension Banach algebra $A\oplus _1 X$ is a BSE Banach algebra if and only if A is a BSE Banach algebra and $X=\{0\}$. Furthermore, we consider $A\oplus _1 X$ as a Banach $A\oplus _1 X$ -module and characterise the BSE module property on $A\oplus _1 X$. We show that $A\oplus _1 X$ is a BSE Banach $A\oplus _1 X$ -module if and only if A and X are BSE Banach A-modules. [ABSTRACT FROM AUTHOR]

In this note we investigate amenability properties in the class of the so‐called DF‐algebras. We also characterize, in terms of the defining sequence of weights, amenable Köthe co‐echelon algebras. [ABSTRACT FROM AUTHOR]

Let A and B be Banach algebras and T: B → A be a continuous homomorphism. n-weak amenability of the Banach algebra A × T B (defined in Bade, W. G., Curtis, P. C., Dales, H. G.: Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55(2), 359-377 (1987)) is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied. [ABSTRACT FROM AUTHOR]