Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions

Häftad, Engelska, 2019

Av J. William Helton, Igor Klep, Scott McCullough, Markus Schweighofer

1 699 kr

Slutsåld

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.

Produktinformation

Utgivningsdatum2019-03-30
Mått178 x 254 x undefined mm
Vikt185 g
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
Antal sidor104
FörlagAmerican Mathematical Society
ISBN9781470434557

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Beräkning och matematisk analys inom Naturvetenskap och teknik

IntroductionDilations and Free Spectrahedral InclusionsLifting and AveragingA Simplified Form for $\vartheta $$\vartheta$ is the Optimal BoundThe Optimality Condition $\alpha =\beta $ in Terms of Beta FunctionsRank versus Size for the Matrix CubeFree Spectrahedral Inclusion GeneralitiesReformulation of the Optimization ProblemSimmons' Theorem for Half IntegersBounds on the Median and the Equipoint of the Beta DistributionProof of Theorem 2.1Estimating $\vartheta (d)$ for Odd $d$.Dilations and Inclusions of BallsProbabilistic Theorems and Interpretations continuedBibliographyIndex.