Communications in Mathematical Physics

, Volume 85, Issue 1, pp 155–176 | Cite as

Group duality and the Kubo-Martin Schwinger condition. II

  • Daniel Kastler
  • Masamichi Takesaki
Article

Abstract

Let ω be an invariant state of theC*-system {\(\mathfrak{A}\),G, α} on a locally compact noncommutative groupG. Assume further that ω is extremal τ-invariant for an action τ of an amenable groupH which is ω-asymptotically abelian and commutes with α. Denoting byFAB,GAB the corresponding two point functions, we give criteria for the fulfillment of the KMS condition with respect to some one parameter subgroup of the center ofG based on the existence of a closable mapT such thatTFAB=GAB for allA,B\(\mathfrak{A}\). Closability is either inL(G),B(G) orC(G), according to clustering properties for τ. The basic mathematical technique is the duality theory for noncompact, noncommutative locally compact groups.

Keywords

Compact Group Duality Theorem Polar Decomposition Group Duality Approximate Identity 

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Daniel Kastler
    • 1
  • Masamichi Takesaki
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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