The KMS condition and spectral passivity in group duality
type: Item
instance of: scholarly article
title: The KMS condition and spectral passivity in group duality
zbMATH Open document ID: 0548.46048
DOI: 10.1016/0022-1236(84)90102-2
published in: Journal of Functional Analysis
publication date: 1984-01-01T00:00:00Z
review text: Let (A,G,\(\alpha)\) be a \(C^*\)-dynamical system, where G is abelian, and let \(\phi\) be an invariant state. Suppose that there is a neighbourhood \(\Omega\) of the identity in \(\hat G\) and a finite constant \(\kappa\) such that \(\prod^{n}_{i=1}\phi (x^*_ ix_ i)\leq\kappa \prod^{n}_{i=1}\phi (x_ ix^*_ i)\) whenever \(x_ i\) lies in a spectral subspace \(R^{\alpha}(\Omega_ i),\) where \(\Omega_ 1+\Omega_ 2+...+\Omega_ n\subseteq\Omega.\) This condition of complete spectral passivity, together with self-adjointness of the left kernel of \(\phi\), ensures that \(\phi\) satisfies the KMS condition for some one- parameter subgroup of G. This extends some concepts considered in the case \(G={\mathbb{R}}\) by \textit{J. de Cannière} [Commun. Math. Phys. 84, 187- 206 (1982; Zbl 0507.46053)] and the author [J. Funct. Anal. 46, 246-257 (1982; Zbl 0485.46032)].
Mathematics Subject Classification ID: 46L55
zbMATH DE Number: 3874013
zbMATH Keywords: spectrally passive
zbMATH Keywords: ground state
zbMATH Keywords: \(C^*\)-dynamical system
zbMATH Keywords: complete spectral passivity
zbMATH Keywords: KMS condition
zbMATH Keywords: one-parameter subgroup
author: Charles J. K. Batty
MaRDI profile type: Publication
full work available at URL: 0022-1236(84)90102-2
OpenAlex ID: W2068394606
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description: scientific article; zbMATH DE number 3874013