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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
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eBook
Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
2019
Overview
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), 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.
Publisher
American Mathematical Society
ISBN
1470434555, 9781470434557
