Spectral Synthesis for Banach Algebras , Ii

0 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...

$varphi$-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...

2 A CERTAIN p - ADIC SPECTRAL THEOREM

3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...