The hyperrigidity of tensor algebras of C⁎-correspondences

Abstract

Given a C * -correspondence X, we give necessary and sufficient conditions for the tensor algebra T + X to be hyperrigid. In the case where X is coming from a topological graph we obtain a complete characterization.

Product systems of C*-correspondences and Takai duality

“…Note however that if one assumes that A is hyperrigid, then (3.3) holds for any locally compact group [24,Theorem 3.6]. In subsequent work [25] we show that the tensor algebra N O r X of a regular product system X over an abelian lattice order (G, P ) is actually hyperrigid and therefore the Hao-Ng isomorphism (3.2) holds for any regular product system X and any locally compact group G.…”

Morita equivalence for operator systems

“…It is not always true that every * -representation π : C * env (X ) → B(H) is the unique extension of π| X . (An example can be constructed for the nonselfajoint operator algebra generated by the Cuntz isometries {s n } n∈N of O ∞ ; see [22,43] for more examples.) An operator space X is called hyperrigid if whenever π is a * -representation of C * env (X ), its restriction π| X to X is a maximal map.…”