## Rocky Mountain Journal of Mathematics

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

#### 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.

#### Article information

Source
Rocky Mountain J. Math., Volume 44, Number 1 (2014), 203-221.

Dates
First available in Project Euclid: 2 June 2014

https://projecteuclid.org/euclid.rmjm/1401740499

Digital Object Identifier
doi:10.1216/RMJ-2014-44-1-203

Mathematical Reviews number (MathSciNet)
MR3216017

Zentralblatt MATH identifier
1297.47011

#### Citation

Levy, Eliahu; Shalit, Orr Moshe. Dilation theory in finite dimensions: The possible, the impossible and the unknown. Rocky Mountain J. Math. 44 (2014), no. 1, 203--221. doi:10.1216/RMJ-2014-44-1-203. https://projecteuclid.org/euclid.rmjm/1401740499

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