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
Author | : J. William Helton |
Publisher | : American Mathematical Soc. |
Total Pages | : 104 |
Release | : 2019-02-21 |
Genre | : Matrices |
ISBN | : 1470434555 |
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An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→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 ϑ(d), expressed as a ratio of Γ functions for d even, of all d×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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