Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the ...

Let U , V , and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplica-tive unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of SV andˆSV , their restrictions to SW andˆSU , their dual coactions, and their full and reduced crossed products. If N (A) denotes the imprimitivity bimodule associated to a ...

Mansfield showed how to induce representations of crossed products of C∗algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable w...

For a maximal coaction δ of a discrete group G on a C-algebra A and a normal subgroup N of G, there are at least three natural A ×δ G δ̂| N − A ×δ| G/N imprimitivity bimodules: Mansfield’s bimodule Y G G/N(A); the bimodule assembled by Ng from Green’s A ×δ G δ̂ G ׈̂ δ| G/N − A ×δ G δ̂| N imprimitivity bimodule X N (A ×δ G) and Katayama duality; and the bimodule assembled from X G N (A ×δ G) and th...

Let A and B be C∗-algebras. We consider a noncommutative convexity in Hilbert A -B-bimodules, called A -B-convexity, as a generalization of C∗-convexity in C∗-algebras. We show that if X is a Hilbert A -B-bimodule, then Mn(X ) is a Hilbert Mn(A )-Mn(B)-bimodule and apply it to show that the closed unit ball of every Hilbert A -B-bimodule is A -B-convex. Some properties of this kind of convexity...

Let (A; G; ; u) be a twisted C*-dynamical system in the sense of Busby and Smith. Then for any closed subgroup H of G, A ;u H is Morita equivalent to C 0 (G=H; A) ~ ;~ u G, where (~ a; ~ u) is the diagonal twisted action. We show that the space of compactly supported bounded Borel functions B c (G; A) can be given a natural pre-imprimitivity bimodule structure which implements the equivalence, ...

The extended Cuntz–Pimsner algebra E(H), introduced by Pimsner, is constructed from a Hilbert B, B–bimodule H over a C∗–algebra B. In this paper we investigate the Haagerup invariant Λ(·) for these algebras, the main result being that Λ(E(H)) = Λ(B) when H is full over B. In particular, E(H) has the completely bounded approximation property if and only if the same is true for B.

We consider C-algebras generated by a single Hilbert bimodule (Pimsner-Toeplitz algebras) and by a product systems of Hilbert bimodules. We give a new proof of a theorem of Pimsner, which states that any representation of the generating bimodule gives rise to a representation of the Pimsner-Toeplitz algebra. Our proof does not make use of the conditional expectation onto the subalgebra invarian...

The C∗-algebra C∗(E) of a directed graph E is generated by partial isometries satisfying relations which reflect the path structure of the graph. In [10], Kumjian and Pask considered the action of a group G on C∗(E) induced by an action of G on E. They proved that if G acts freely and E is locally finite, then the crossed product C∗(E) × G is Morita equivalent to the C∗-algebra of the quotient ...