Dilation theory in finite dimensions: The possible, the impossible and the unknown

Eliahu Levy, Orr Moshe Shalit

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra It turns out that some interesting and simple results can be obtained. These results can be used to give very elementary proofs of sharpened versions of some von Neumann type inequalities, as well as some other striking consequences about polynomials and matrices. Exploring the limits of the finite dimensional approach sheds light on the difference between those techniques and phenomena in operator theory that are inherently infinite dimensional, and those that are not.

Original languageEnglish
Pages (from-to)203-221
Number of pages19
JournalRocky Mountain Journal of Mathematics
Volume44
Issue number1
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

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