Roots in Operator and Banach Algebras

被引：0
作者：
David P. Blecher
Zhenhua Wang
机构：
[1] University of Houston,Department of Mathematics
来源：
Integral Equations and Operator Theory | 2016年 / 85卷
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; Primary 47A64; 47L10; 47L30; 47B44; Secondary 15A24; 15A60; 47A12; 47A60; 47A63; 49M15; 65F30;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：63 / 90
页数：27
相关论文
共 37 条
[1]  
Bartle R.G.(1955)Newton’s method in Banach spaces Proc. Am. Math. Soc. 6 827-831
[2]  
Bearden C.A.(2014)On positivity and roots in operator algebras J. Integr. Equ. Oper. Theory 79 555-566
[3]  
Blecher D.P.(1997)How and why to solve the operator equation Bull. Lond. Math. Soc. 29 1-21
[4]  
Sharma S.(2005)Algorithms for the matrix pth root Numer. Algorithms 39 349-378
[5]  
Bhatia R.(2015)Real positivity and approximate identities in Banach algebras Pac. J. Math. 277 1-59
[6]  
Rosenthal P.(2011)Operator algebras with contractive approximate identities J. Funct. Anal. 261 188-217
[7]  
Bini D.A.(2013)Operator algebras with contractive approximate identities II J. Funct. Anal. 264 1049-1067
[8]  
Higham N.J.(2014)Order theory and interpolation in operator algebras Studia Math. 225 61-95
[9]  
B. Meini(2010)Numerical ranges of the powers of an operator J. Math. Anal. Appl. 365 458-466
[10]  
Blecher D.P.(2008)A functional calculus based on the numerical range: applications Linear Multilinear Algebra 56 81-103
1234