Ebook: Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
Author: J. William Helton, Igor Klep, Scott McCullough
- Tags: Matrices., Matrix inequalities.
- Series: Memoirs of the American Mathematical Society Ser.
- Year: 2018
- Publisher: American Mathematical Society
- City: Providence, United States
- Edition: 1
- Language: English
- pdf
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.
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