Rocky Mountain Journal of Mathematics

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

Eliahu Levy and Orr Moshe Shalit

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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.

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

First available in Project Euclid: 2 June 2014

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Zentralblatt MATH identifier

Primary: 47A20: Dilations, extensions, compressions
Secondary: 15A45: Miscellaneous inequalities involving matrices 47A57: Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]


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.

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