C*-Envelope and Dilation Theory of Semigroup Dynamical Systems

Li, Boyu

doi:10.1007/s00020-021-02636-6

Cited by 2 publications

(2 citation statements)

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“…(2) For every p ∈ P and a ∈ A, Remark 4.11. The connection between the covariance relations V (p)π(a) = π(α p (a))V (p) and V (p)π(a)V (p) * = π(α p (a)) is further explored in [23], where it is shown that when the semigroup is abelian, the former relation can be dilated to the latter one.…”

Section: Naimark Dilation On Semigroup Dynamical Systemsmentioning

confidence: 99%

“…This construction also motivated the study of boundary quotients, an analogue of the Cuntz algebras in the realm of semigroup C * -algebras. On the other hand, in the realm of non-self-adjoint operator algebras, semigroup dynamical systems play a central role in the construction of various semicrossed product algebras and the computation of their C * -envelope [16,13,12,23]. Dilation theory is often a useful tool in these studies.…”

Section: Introductionmentioning

confidence: 99%

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Dilation theory for right LCM semigroup dynamical systems

Laca,

2021

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This paper examines actions of right LCM semigroups by endomorphisms of C*-algebras that encode an additional structure of the right LCM semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing that these representations can be dilated if and only if the map on the C * -algebra is unital and completely positive. This generalizes earlier results about dilations of right LCM semigroups of contractions. In addition, we also give sufficient conditions under which a contractive covariant representation of a right LCM system can be dilated to an isometric representation of the boundary quotient.

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Section: Naimark Dilation On Semigroup Dynamical Systemsmentioning

confidence: 99%