On reducible nonmonic matrix polynomials with general and nonnegative coefficients

被引：0

作者：

Foerster, K. -H. ^{[1
]}

Nagy, B. ^{[2
]}

机构：

[1] Tech Univ Berlin, Inst Math, MA 6-4, D-10623 Berlin, Germany

[2] Univ Technol & Econ, Inst Math, Dept Anal, H-1521 Budapest, Hungary

来源：

OPERATOR THEORY IN INNER PRODUCT SPACES | 2007年 / 175卷

关键词：

reducible matrix polynomials; block triangular operator coefficients; (entrywise) nonnegative matrix coefficients; nonnegative matrix roots;

D O I：

10.1007/978-3-7643-8270-4_6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider nonmonic quadratic polynomials acting on a general or on a finite-dimensional linear space as a continuation of our work in [7,8]. Conditions are given for the existence of right roots, if the coefficient operators have lower block triangular representations. In the finite-dimensional case we consider (in a certain sense, entrywise) nonnegative coefficient matrices in the general (reducible) case, and extend several earlier results from the case of irreducible coefficients. In particular, we generalize results of Gail, Hantler and Taylor [9]. We show that our general methods are sufficiently strong to prove a remarkable result by Butler, Johnson and Wolkowicz; [3], proved there by ingenious ad hoc methods.

引用

页码：95 / 109

页数：15