Entropy-Invariants of Dynamical Systems and Perturbations of Operators

Dan Voiculescu
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Dan Voiculescu: University of California, Department of Mathematics

A chapter in Mathematical Physics X, 1992, pp 303-307 from Springer

Abstract: Abstract In [12] we proved a sharp extension to the case of commuting n-tuples, of the well-known invariance of absolutely continuous spectra in trace-class scattering theory. Our proof relied on invariants k ℐ (τ)(ℐ a normed ideal, τ an n-tuple of operators), playing the role of a ”size ℐ”-dimensional measure of τ. We recently found the entropy of dynamical systems is related to k ℐ (τ) with ℐ = C ∞ - the Macaev ideal. This report is about k ℐ (τ) and its use in constructing entropy-line invariants. We also explain the connection between k 1(τ) and the entropy of Bogoliubov automorphisms ([11]).

Keywords: Normed Ideal; London Mathematical Society Lecture Note; Pure Point Spectrum; Finite Rank Operator; Quasifree State (search for similar items in EconPapers)
Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-77303-7_26

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DOI: 10.1007/978-3-642-77303-7_26

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