In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group Iso (U) of isometries of Urysohn’s universal complete separable metric space U, equipped with the compact-open topology, acts upon an arbitrary compact space, it has a fixed point. The ...

Abstract Amenable actions of locally compact groups on von Neumann algebras are investigated by exploiting the natural module structure crossed product over Fourier algebra acting group. The resulting characterization injectivity for products generalizes a result Anantharaman-Delaroche discrete groups. $C^*$ -algebras in same way, and amenability action is related to nuclearity corresponding pr...

We give a construction which takes a rank two incidence geometry with three points on a line and returns a geometry of the same type, i.e., with three points on a line. It is also demonstrated that embeddings of the original geometry can be extended to the new geometry. It is shown that the family of dual polar spaces of type Sp(2n, 2) arise recursively from the construction starting with the g...

in 2005, a. abdollahi and a. rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. in thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. we have extend the previous knownresults to semigroups and groups satisfying this concept.

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

We present a new approach to the amenability of groupoids (both in the measure theoretical and the topological setups) based on using Markov operators. We introduce the notion of an invariant Markov operator on a groupoid and show that the Liouville property (absence of non-trivial bounded harmonic functions) for such an operator implies amenability of the groupoid. Moreover, the groupoid actio...

In this paper, we study the L functions on U(2n)/O(2n) and Mp(n,R). We relate them using the oscillator representation. We first study some isometries between various L spaces using the compactification we defined in [6]. These isometries were first introduced by Betten-Ólafsson in [3] . We then give a description of the matrix coefficients of the oscillator representation ω in terms of algebra...

‎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...

When 2−1/Q<p≤2, we establish the Cloc0,1 and Cloc1,α-regularities of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in Heisenberg group Hn, where Q=2n+2 is homogeneous dimension Hn.

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenabl...