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 language | English |
|---|---|
| Pages (from-to) | 203-221 |
| Number of pages | 19 |
| Journal | Rocky Mountain Journal of Mathematics |
| Volume | 44 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2014 |
| Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics