Perturbations of Operators, Connections with Singular Integrals, Hyperbolicity and Entropy

Dan Voiculescu
Additional contact information
Dan Voiculescu: University of California, Department of Mathematics

A chapter in Harmonic Analysis and Discrete Potential Theory, 1992, pp 181-191 from Springer

Abstract: Abstract We have studied in a series of papers ([10], [11], [12]) perturbations of Hilbert space operators using a certain invariant k J (τ), where J is a normed ideal of operators and τ is an n-tuple of operators. This number can be viewed as a “size J”- dimensional measure of τ. Frequently, evaluation of k J (τ) is related to the asymptotic of eigenvalues of certain singular integrals. In the case of translation operators in the regular representation of a discrete group G the number k J is related to the analogue of Yamasaki’s hyperbolicity condition on the Cayley graph of G with respect to the norm defining J. Quite recently, we have shown that in case J is the Macaev ideal $$C_\infty ^ - $$ , the invariant k J is related to the entropy of dynamical systems ([13]). Also in the case of the Macaev ideal, the existence of a random walk with positive entropy on a discrete group implies a hyperbolicity condition [14].

Keywords: Fractional Dimension; Discrete Group; Singular Integral; Cayley Graph; SELFADJOINT Operator (search for similar items in EconPapers)
Date: 1992
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-2323-3_14

Ordering information: This item can be ordered from
http://www.springer.com/9781489923233

DOI: 10.1007/978-1-4899-2323-3_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().