Dilations, Linear Matrix Inequalities, the Matrix Cube Problem, and Beta Distributions
Dilations, Linear Matrix Inequalities, the Matrix Cube Problem,
and Beta Distributions
by J. William Helton, Igor Klep
English | 2019 | ISBN: 1470434555 | 118 Pages | PDF | 1.03 MB
and Beta Distributions
by J. William Helton, Igor Klep
English | 2019 | ISBN: 1470434555 | 118 Pages | PDF | 1.03 MB
An operator $C$ on a Hilbert space $mathcal H$ dilates to an operator $T$ on a Hilbert space $mathcal K$ if there is an isometry $V:mathcal Hto mathcal K$ such that $C= V* TV$. A main result of this paper is, for a positive integer $d$, the simultaneous dilation, up to a sharp factor $vartheta (d)$, expressed as a ratio of $Gamma $ functions for $d$ even, of all $dtimes d$ symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.