Dilation theory in finite dimensions: the possible, the impossible and the unknown
By Eliahu Levy, Orr Shalit. 2010
47 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/23edc0850ef45c6acf07575c59c9e77717a3f915
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
- K. Davidson
- Orr Shalit
- B. Solel
- Gelu Popescu
- Michael Hartz
- E. Shamovich
- Guy Salomon
- Elias G. Katsoulis
Citations in the corpus
- Dilations, inclusions of matrix convex sets, and completely positive maps (2016, background): “The proof is based on some ideas from [9, 21, 22].”