As an application we give necessary and sufficient conditions in order that (A, P) is isomorphic to (Oλ(G), Σ) with λ the regular representation of a compact and metrizable group G and Σ the set of endomorphisms induced by an irreducible decomposition of λ.
This completely generalizes a well-known result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group.
First of all, the interest is focused on the full (C^* -algebra (C^* -algebraon the reduC^* (C^*)-alGebrand(C_r^*(G)) generated by the left (on, whathes essentially the same, reducedregular representation of a group.
A Cayley graph X = C a y(G,S) is called normal for G if the right regular representation of G is a normal subgroup of the automorphism group of X (see[1]).
We prove a theorem of Dixmier and Malliavin type for analytic vectors of bounded representations of (R,+): Let (π,E) be a bounded representation of (R,+) in a Banach space E and let A be the convolution algebra of analytic vectors for the left regular representation of R on L1(R), then A∗A="A and π(A E="Eω.
Every finite group is isomorphic to a matrix group, as one can see by considering the regular representation of the symmetric group.
Let G be a locally compact group and VN G) be the von Neumann algebra generated by the left regular representation of G. Let UCB denote the C*-subalgebra generated by operators in VN(G) with compact support.
Using Takai duality we establish a stable isomorphismA⋊αΣ∼s(A⊗K(G,Σ,μ))⋊α⊗AdρG, where K(G,Σ,μ) denotes the compact operators in the CSL algebra AlgL(G,Σ,μ) and ρ denotes the right regular representation of G.
