THE KMS CONDITION AND SPECTRAL PASSIVITY IN GROUP DUALITY

Journal article

Let (A, G, α) be a C*-dynamical system, where G is abelian, and let φ be an invariant state. Suppose that there is a neighbourhood Ω of the identity in G ̂ and a finite constant κ such that Πi = 1n φ(xi*xi) ≤ κ Πi = 1n φ(xixi*) whenever xi lies in a spectral subspace Rα(Ωi), where Ω1 + ... + Ωn ⊂ Ω. This condition of complete spectral passivity, together with self-adjointness of the left kernel of φ, ensures that φ satisfies the KMS condition for some one-parameter subgroup of G. © 1984.

Authors: Batty, C

• Publication status: Published
• Journal: JOURNAL OF FUNCTIONAL ANALYSIS
• Volume: 57
• Issue: 3
• Pages: 233-243
• Publication date: 1984-01-01
• DOI: 10.1016/0022-1236(84)90102-2
• EISSN: 1096-0783
• ISSN: 0022-1236
• Language: English