Date: 16 Sep 2006

Quasi-product states on C*-algebras

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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.