ENTROPY OF DYNAMIC-SYSTEMS AND PERTURBATIONS OF OPERATORS

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. © 1991, Cambridge University Press. All rights reserved.