In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...

Using a “3 by 3 matrix trick” we previously showed that multiplication in a C*-algebra A, an algebraic structure, is determined by the geometry of the C*-algebra of the 3 by 3 matrices with entries from A, M3(A). As an application of this algebra-geometry duality we now construct an order theoretic based duality theory for all groups which are either locally compact abelian or finite. This cons...

let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p

We study the centraliser of locally compact group extensions of er-godic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed. Smooth versions of some of the constructions are also given. §0 Introduction Let T be an ergodic probability preserving transfor...

For Pontryagin’s group duality in the setting of locally compact topological Abelian groups, the topology on the character group is the compact open topology. There exist at present two extensions of this theory to topological groups which are not necessarily locally compact. The first, called the Pontryagin dual, retains the compact-open topology. The second, the continuous dual, uses the cont...

Abstract We show that if a locally compact group $G$ is non-abelian, then the amenability constant of its Fourier algebra $\geq 3/2$, extending result [9] who proved this holds for finite non-abelian groups. Our lower bound, which known to be best possible, improves on results by previous authors and answers question raised [16]. To do this, we study minorant constant, related anti-diagonal in ...

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.