Dilations, Linear Matrix Inequalities, the Matrix Cube...

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Dilations, Linear Matrix Inequalities,...

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

J. William Helton, Igor Klep, Scott McCullough

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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.

Jahr:

2018

Auflage:

1

Verlag:

American Mathematical Society

Sprache:

english

Seiten:

118

ISBN 10:

1470449471

ISBN 13:

9781470449476

Serien:

Memoirs of the American Mathematical Society Ser.

Datei:

PDF, 1012 KB

IPFS:

,

english, 2018

Herunterladen (pdf, 1012 KB)

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