Polynomial bounds for small matrices

被引：5

作者：

Crouzeix, Michel ^{[1
]}

Gilfeather, Frank ^{[2
]}

Holbrook, John ^{[3
]}

机构：

[1] Univ Rennes, Dept Math, Rennes, France

[2] Univ New Mexico, Dept Math & Stat, Albuquerque, NM 87131 USA

[3] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

47L25; 46L07; polynomially bounded matrices; completely bounded norm; HILBERT-SPACE; DISTORTION COEFFICIENTS; OPERATORS; CONTRACTION;

D O I：

10.1080/03081087.2013.777439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The polynomial bound of a Hilbert space operator is the quantity . One of the Halmos 'Ten problems' asked whether implies that is similar to a contraction. This question was settled in the negative by Pisier after many years. The finite-dimensional version of the problem asks to what extent can be exceeded by . We establish some general criteria for the equality and show that can occur even for matrices.

引用

页码：614 / 625

页数：12

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