Non-Commutative Polynomials with Convex Level Slices

被引：3

作者：

Dym, Harry ^{[1
]}

Helton, J. William ^{[2
]}

McCullough, Scott ^{[3
]}

机构：

[1] Weizmann Inst Sci, Dept Math, IL-7610001 Rehovot, Israel

[2] Univ Calif San Diego, Dept Math, San Diego, CA 92103 USA

[3] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2017年 / 66卷 / 06期

基金：

美国国家科学基金会;

关键词：

ALGEBRAIC-GEOMETRY; MATRIX CONVEXITY; QUOTIENTS; SIGNATURE;

D O I：

10.1512/iumj.2017.66.6219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study the structure of symmetric polynomials p(a, x) in freely noncommuting symmetric variables a = (a(1), ..., a((g) over tilde)) and x = (x(1), ..., x(g)) such that the set of matrix tuples.

引用

页码：2071 / 2135

页数：65

共 14 条

[1] QUASI-CONVEX FREE POLYNOMIALS [J].

Balasubramanian, S. ;

McCullough, S. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (08) :2581-2591

[2] Matrix inequalities: A symbolic procedure to determine convexity automatically [J].

Camino, JF ;

Helton, JW ;

Skelton, RE ;

Ye, JP .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2003, 46 (04) :399-454

[3]

de Oliveira MC, 2009, IMA VOL MATH APPL, V149, P17

[4] The Hessian of a noncommutative polynomial has numerous negative eigenvalues [J].

Dym, Harry ;

Helton, J. William ;

McCullough, Scott .

JOURNAL D ANALYSE MATHEMATIQUE, 2007, 102 (1) :29-76

[5] Irreducible noncommutative defining polynomials for convex sets have degree four or less [J].

Dym, Harry ;

Helton, William ;

McCullough, Scott .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2007, 56 (03) :1189-1231

[6] NON-COMMUTATIVE VARIETIES WITH CURVATURE HAVING BOUNDED SIGNATURE [J].

Dym, Harry ;

Helton, J. William ;

McCullough, Scott .

ILLINOIS JOURNAL OF MATHEMATICS, 2011, 55 (02) :427-464

[7] CLASSIFICATION OF ALL NONCOMMUTATIVE POLYNOMIALS WHOSE HESSIAN HAS NEGATIVE SIGNATURE ONE AND A NONCOMMUTATIVE SECOND FUNDAMENTAL FORM [J].

Dym, Harry ;

Greene, J. M. ;

Helton, J. W. ;

McCullough, S. A. .

JOURNAL D ANALYSE MATHEMATIQUE, 2009, 108 :19-59

[8] Matrix convexity: Operator analogues of the bipolar and Hahn-Banach theorems [J].

Effros, EG ;

Winkler, S .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 144 (01) :117-152

[9]

Farenick D, 2012, MATH SCAND, V111, P210

[10] Non-commutative Partial Matrix Convexity [J].

Hay, Damon M. ;

Helton, J. William ;

Lim, Adrian ;

McCullough, Scott .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (06) :2815-2842

← 1 2 →