应用泛函分析学报2005，Vol.7Issue(3)：193-197,5.
关于Aluthge变换的数值域
Numerical Range of the Aluthge Transform
摘要
Abstract
For any bounded linear operator A on a Hilbert space ( ), if A = V|A| is a polar decomposition of A, the Aluthge transform (~A) and the · -Aluthge transform (~A)(·) of A are defined by (~A)= |A|1/2 V|A|1/2 and (~A)(·) = |A· |1/2 V|A· |1/2, respectively. Denote by W((~A)) and W((~A)(·)) the numerical ranges of (~A) and (~A)(·), respectively. In this note, we prove that W((~A)) = W((~A)(·)). This confirms a conjecture of Wu.关键词
Aluthge变换/数值域/谱Key words
aluthge transform/numerical range/spectrum分类
数理科学引用本文复制引用
刘秀梅,杨新兵,杜鸿科..关于Aluthge变换的数值域[J].应用泛函分析学报,2005,7(3):193-197,5.基金项目
This subject is supported by the National Natural Science Foundation of China (10071047) （10071047）
