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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Araki, A.L. Carey, D.E. Evans. On On+1. J. Operator Theory (in press).
H. Araki, R. Haag, D. Kastler, M. Takesaki. Extension of states and chemical potential. Commun. math. Phys. 53 (1977), 97–134.
O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics II. Springer Verlag. Berlin, Heidelberg, New York 1981.
J. Cuntz. Simple C*-algebras generated by isometries. Commun. math. Phys. 57 (1977), 173–185.
J. Cuntz, W. Krieger, A class of C*-algebras and topological Markov chains. Inventiones Math. 56 (1980), 251–258.
D.E. Evans. On On. Publ.RIMS Kyoto Univ. 16 (1980), 915–927.
D.E. Evans. Entropy of automorphisms of AF algebras. Publ. RIMS Kyoto Univ. 18 (1982), 1045–1051.
D.E. Evans. The C*-algebras of topological Markov chains. Lecture notes. Tokyo Metropolitan University, 1983.
S. Kakutani. On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214–222.
W. Krieger. On constructing non-isomorphic hyperfinite factors of type III. J. Func. Analysis. 6 (1970), 97–109.
C.C. Moore. Invariant measures on product spaces. Proc. of the Fifth Berkeley Symposium on Math. Stat. and Probability. Vol. II, part II, 447–459 (1967).
E. Seneta. Non negative matrices and Markov chains. Springer-Verlag. Berlin, Heidelberg and New York. (2nd edition), 1981.
S. Stratila, D. Voiculescu. Representations of AF algebras and of the group U(∞). Lecture notes in Mathematics. Springer-Verlag, vol. 486. Berlin, Heidelberg and New York, 1975.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verleg
About this paper
Cite this paper
Evans, D.E. (1985). Quasi-product states on C*-algebras. In: Araki, H., Moore, C.C., Stratila, ÅžV., 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
Download citation
DOI: https://doi.org/10.1007/BFb0074883
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15643-7
Online ISBN: 978-3-540-39514-0
eBook Packages: Springer Book Archive