Dynamical Systems from Function Algebras

Pennings, Tim; Peters, J.A.F.

doi:10.2307/2046738

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Dynamical Systems1

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2009

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“…Definition 1. Given a dynamical system (X, ϕ) we will say (following the terminology of [12]) the dynamical system (Y, ψ) is an extension of (X, ϕ) in case there is a continuous surjection p : Y → X such that the the diagram…”

Section: Dynamical Systemsmentioning

confidence: 99%

The 𝐶*-envelope of a semicrossed product and nest representations

Peters¹

2009

Operator Structures and Dynamical Systems

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Let X be compact Hausdorff, and ϕ : X → X a continuous surjection. Let A be the semicrossed product algebra corresponding to the relation f U = U f • ϕ or to the relation U f = f • ϕU. Then the C * -envelope of A is the crossed product of a commutative C * -algebra which contains C(X) as a subalgebra, with respect to a homeomorphism which we construct. We also show there are"sufficiently many" nest representations.

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Section: Dynamical Systemsmentioning

confidence: 99%