Let (G,G′) ⊂ Sp(W) be an irreducible real reductive dual pair of type I in stable range, with G the smaller member. In this note, we prove that all irreducible genuine representations of G̃ occur in the Howe correspondence. The proof uses structural information about the groups forming a reductive dual pair and estimates of matrix coefficients.

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In part...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded th...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

A proper embedding of a graph G in a pseudosurface P is an embedding in which the regions of the complement of G in P are homeomorphic to discs and pinchpoints of P correspond to vertices in G; we say that a proper embedding of G in P is self dual if there exists an isomorphism from G to its topological dual. We show that each graph that has a possibility of being self-dual embeddable in a pseu...

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T ∗ in the dual graph G∗ such that T and T ∗ do not intersect. We show that it is not always possible to find T in G such that the diameters of T and T ∗ are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.