TY - JOUR

T1 - Dilation theory in finite dimensions

T2 - The possible, the impossible and the unknown

AU - Levy, Eliahu

AU - Shalit, Orr Moshe

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84897048317&partnerID=8YFLogxK

U2 - 10.1216/RMJ-2014-44-1-203

DO - 10.1216/RMJ-2014-44-1-203

M3 - Article

AN - SCOPUS:84897048317

VL - 44

SP - 203

EP - 221

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 1

ER -