Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions
J. William Helton, Igor Klep, Scott McCullough
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.
ปี:
2018
ฉบับพิมพ์ครั้งที่:
1
สำนักพิมพ์:
American Mathematical Society
ภาษา:
english
จำนวนหน้า:
118
ISBN 10:
1470449471
ISBN 13:
9781470449476
ซีรีส์:
Memoirs of the American Mathematical Society Ser.
ไฟล์:
PDF, 1012 KB
IPFS:
,
english, 2018