Dilations, Linear Matrix Inequalities, the Matrix Cube Problem, and Beta Distributions
Description:... 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.
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