Cargando…
Dilations, linear matrix inequalities, the matrix cube problem, and beta distributions /
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 H\to \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), expresse...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, RI :
American Mathematical Society,
2019.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1232. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction
- Dilations and Free Spectrahedral Inclusions
- Lifting and Averaging
- A Simplified Form for $\vartheta $
- $\th $ is the Optimal Bound
- The Optimality Condition $\myal =\mybe $ inTerms of Beta Functions
- Rank versus Size for the Matrix Cube
- Free Spectrahedral Inclusion Generalities
- Reformulation of the Optimization Problem
- Simmons' Theorem for Half Integers
- Bounds on the Median and the Equipoint of the Beta Distribution
- Proof of Theorem 1.2
- Estimating $\th (d)$ for Odd $d$
- Dilations and Inclusions of Balls
- Probabilistic Theorems and Interpretations Continued