| Description |
1 online resource (v, 106 pages) |
| Series |
Memoirs of the American Mathematical Society, 1947-6221 ; volume 257, number 1232 |
|
Memoirs of the American Mathematical Society ; no. 1232. 1947-6221
|
| Contents |
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 |
| Summary |
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= V̂* 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 d\times d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space |
| Notes |
"January 2019, volume 257, number 1232 (second of 6 numbers)." |
|
"Keywords:Dilation, completely positive map, linear matrix inequality, spectrahedron, free spectrahedron, matrix cube problem, binomial distribution, beta distribution, robust stability, free analysis"--Online information |
| Bibliography |
Includes bibliographical references (pages 101-104 and index |
| Notes |
Print version record |
| Subject |
Matrices.
|
|
Matrix inequalities.
|
|
MATHEMATICS -- Algebra -- Intermediate.
|
|
Matrices
|
|
Matrices
|
|
Matrix inequalities
|
| Form |
Electronic book
|
| Author |
Helton, J. William, 1944- author.
|
| ISBN |
1470449471 |
|
9781470449476 |
|
