Roots in Operator and Banach Algebras

被引：4

作者：

Blecher, David P. ^{[1
]}

Wang, Zhenhua ^{[1
]}

机构：

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2016年 / 85卷 / 01期

基金：

美国国家科学基金会;

关键词：

Roots; fractional powers; geometric mean; sign of operator; Newton method for roots; binomial method for square root; accretive operator; sectorial operator; nonselfadjoint operator algebra; numerical range; functional calculus; NUMERICAL RANGES; POWERS; MATRICES;

D O I：

10.1007/s00020-015-2272-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that several known facts concerning roots of matrices generalize to operator algebras and Banach algebras. We show for example that the so-called Newton, binomial, Visser, and Halley iterative methods converge to the root in Banach and operator algebras under various mild hypotheses. We also show that the 'sign' and 'geometric mean' of matrices generalize to Banach and operator algebras, and we investigate their properties. We also establish some other facts about roots in this setting.

引用

页码：63 / 90

页数：28

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