C⁎-stability of discrete groups

Structural Properties of Inner Amenable Discrete Groups

Stability Results for C∗-unitarizable Groups

We say that a locally compact group G is C∗-unitarizable if its full group C∗-algebra C∗(G) satisfies Kadison’s similarity problem (SP), i.e. every bounded representation of C∗(G) on a Hilbert space is similar to a *representation. We prove that locally compact and unitarizable groups are C∗-unitarizable. For discrete groups, we prove that C∗-unitarizable passes to quotients. Moreover, a given ...

On C∗-Algebras Associated to Certain Endomorphisms of Discrete Groups

Let α : G → G be an endomorphism of a discrete amenable group such that [G : α(G)] < ∞. We study the structure of the C∗ algebra generated by the left convolution operators acting on the left regular representation space, along with the isometry of the space induced by the endomorphism.

structural properties of inner amenable discrete groups

Stability of additive functional equation on discrete quantum semigroups

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...