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

Author:   J. William Helton ,  Igor Klep ,  Scott McCullough ,  Markus Schweighofer
Publisher:   American Mathematical Society
ISBN:  

9781470434557


Pages:   104
Publication Date:   30 March 2019
Format:   Paperback
Availability:   In Print   Availability explained
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Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions


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Overview

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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Author:   J. William Helton ,  Igor Klep ,  Scott McCullough ,  Markus Schweighofer
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.185kg
ISBN:  

9781470434557


ISBN 10:   1470434555
Pages:   104
Publication Date:   30 March 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

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J. William Helton, University of California, San Diego, California. Igor Klep, The University of Auckland, New Zealand. Scott McCullough, University of Florida, Gainesville, Florida. Markus Schweighofer, Universitat Konstanz, Germany.

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