A locally compact group G is compact if and only if L(G) is an ideal in L(G). On the other hand, the Fourier algebra A(G) of G is an ideal in A(G)∗∗ if and only if G is discrete. We show that both results are special cases of one general theorem on locally compact quantum groups in the sense of J. Kustermans and S. Vaes: a von Neumann algebraic quantum group (M,Γ) is compact if and only if M∗ i...

in this short note, we have given a short proof for the existence of the haar measure on commutative locally compact hypergroups based on functional analysis methods by using markov-kakutani fixed point theorem.

Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...

Let G be a locally compact topological group. A lattice in G is a discrete subgroup Γ such that Γ\G carries a finite G–invariant measure, and Γ is uniform or cocompact if Γ\G is compact. Lattices in Lie groups have been well-studied. See, for example, Raghunathan [48], and for open problems the section on “Lattices in Lie groups” in this wiki. Much less is known about lattices in other locally ...

In this note we study the dynamics of the natural evaluation action of the group of isometries G of a locally compact metric space (X, d) with one end. Using the notion of pseudocomponents introduced by S. Gao and A. S. Kechris we show that X has only finitely many pseudo-components exactly one of which is not compact andG acts properly on this pseudo-component. The complement of the non-compac...

The crossed products of locally C-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C-algebra is proved. 2000 AMS Mathematics subject classification. Primary 46L05, 46L55.

If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped with the compact-open topology. For subsets A and B of X we define [A, B] = {h ∈ H(X) : h(A) ⊂ B}, and we recall that the topology on H(X) is generated by the subbasis SX = {[K , O] : K compact, O open in X}. If X is a compact Hausdorff space, then H(X) is a topological group, that is, composition...