Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions (Memoirs of the American Mathematical Society)

Helton, J. William; Klep, Igor; Mccullough, Scott; Schweighofer, Markus

ISBN 10: 1470434555 / ISBN 13: 9781470434557

Published by American Mathematical Society, 2019

About this Item

8vo (25 cm), VI, 106 pp. Laminated wrappers.

Seller Inventory # 008518

Bibliographic Details

• Title: Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions (Memoirs of the American Mathematical Society)
• Publisher: American Mathematical Society
• Publication Date: 2019
• Language: English
• ISBN 10: 1470434555
• ISBN 13: 9781470434557
• Binding: Soft cover
• Condition: New
• Seller catalogs:
  • Mathematics

About this title

Synopsis

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 $V:mathcal Hto mathcal K$ 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 $dtimes d$ symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.