0 Spectral Synthesis for Banach Algebras , Ii

Spectral Synthesis for Banach Algebras , Ii

This paper continues the study of spectral synthesis and the topologies τ ∞ and τ r on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C *-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of τ ∞. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffne...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

An Example on Ordered Banach Algebras

Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...

$varphi$-Connes amenability of dual Banach algebras

‎Generalizing the notion of character amenability for Banach‎ ‎algebras‎, ‎we study the concept of $varphi$-Connes amenability of‎ ‎a dual Banach algebra $mathcal{A}$ with predual $mathcal{A}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{A}$ onto $Bbb C$‎ ‎that lies in $mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎follo...