Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
Feb 2019 · American Mathematical Soc.
Ebook
104
Pages
About this ebook
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.
About the author
J. William Helton: University of California, San Diego, California,
Igor Klep: The University of Auckland, Auckland, New Zealand,
Scott McCullough: University of Florida, Gainesville, Florida,
Markus Schweighofer: Universität Konstanz, Konstanz, Germany
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