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Entropy of dynamical systems and perturbations of operators

Published online by Cambridge University Press:  19 September 2008

Dan Voiculescu
Dan Voiculescu
Affiliation:
Department of Mathematics, University of California, Berkeley CA 94720, USA
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Extract

In the papers [9, 10, 3, 11] on perturbations of Hilbert space operators, we studied an invariant (τ) where is a normed ideal of compact operators and τ a family of operators. The size of an ideal for which (τ) vanishes or does not vanish is an upper, respectively lower, bound for a kind of dimension of τ. In the case of systems of commuting self-adjoint operators τ, the results of [9,3] relate (τ) with (an ideal slightly smaller than the Schatten von Neumann class ) to the way the spectral measure of τ compares to p-dimensional Hausdorff measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 779 - 786
Copyright
Copyright © Cambridge University Press 1991

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References

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