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Quasi-product states on C*-algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 1132)

Abstract

We introduce and study a class of Markov measures, which we call quasi-product measures, on compact totally disconnected path spaces, and consider the induced states, called quasi-product states on the associated unital AF algebras and the infinite C*-algebras 0 A associated with a topological Markov chain A. For product spaces, and UHF algebras these are precisely product measures and product states respectively. In particular, we give sufficient conditions which ensure that the gauge group is weakly outer in certain quasi-product weights on the stablised C*-algebra of 0 A.

Keywords

  • Gauge Group
  • Product Measure
  • Full Shift
  • Markov Measure
  • Topological Markov Chain

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© 1985 Springer-Verleg

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Evans, D.E. (1985). Quasi-product states on C*-algebras. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074883

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  • DOI: https://doi.org/10.1007/BFb0074883

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

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