广义Aluthge变换的极大数值域
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摘要
设H为复可分无限维Hilbert空间,■及■分别为H上有界线性算子A的广义Aluthge变换及广义~*-Aluthge变换.对任意复数λ,利用算子分块技巧证明了■及■的范数相等且极大数值域相等,并进一步给出了■及■内导子范数的关系.
Let H be an infinite separable Hilbert space and A be a bounded linear operator on H. The generalized Aluthge transform and the generalized~*-Aluthge transform of A are denoted by ■, respectively, where t∈(0, 1). By the method of operational partitioning, for any complex λ, the norm and maximal numerical range of ■ are considered, and the relationship between the norm of the inner derivation of ■ is given.
Let H be an infinite separable Hilbert space and A be a bounded linear operator on H. The generalized Aluthge transform and the generalized~*-Aluthge transform of A are denoted by ■, respectively, where t∈(0, 1). By the method of operational partitioning, for any complex λ, the norm and maximal numerical range of ■ are considered, and the relationship between the norm of the inner derivation of ■ is given.
引文
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[15] ZHANG Y,JI G X.Spectral Properties of the Generalized Aluthge Transform [J].Acta Analysis Functionalis Applicata,2008,10(2):116-122.
[16] 刘秀梅,杨新兵.关于广义Aluthge变换的数值域 [J].纯粹数学与应用数学,2010,26(1):111-114.
[3] JUNG I B,KO E,PEARCY C.Aluthge Transforms of Operators [J].Integral Equations and Operator Throry,2000,37:437-448.
[4] 刘秀梅,杨新兵.广义Aluthge与广义*-Aluthge变换的一些性质 [J].南阳师范学院学报,2007,6(9):7-9.
[5] JUNG I B,KO E,PEARCY C.Spectral Pictures of Aluthge Tranforms of Operators [J].Integral Equations and Operator Theory,2001,40:52-60.
[6] 单钰琦,候国林,秦文青.有界线性算子广义Aluthge变换的谱分析 [J].内蒙古大学学报(自然科学版),2014,45(1):1-5.
[7] 刘妮,李炳杰,郭艳鹂.广义Aluthge变换的Drazin逆 [J].空军工程大学学报(自然科学版),2014,15(3):93-95.
[8] LIU X M,JI G X.Some Properties of the Generalized Aluthge Transform [J].Nihonkai Math J,2004,15(1):101-107.
[9] 刘妮,李炳杰.Aluthge变换的本性极大数值域 [J].安徽大学学报(自然科学版),2016,40(2):9-13.
[10] 李泽,刘妮,吉国兴.Aluthge变换值域中的代数算子和平移性质 [J].陕西师范大学学报(自然科学版),2007,35(4):5-8.
[11] WU P Y.Numerical Range of Aluthge Transform of Operator [J].Linear Algebra and its Applications,2002,357:295-298.
[12] LIU X M,YANG X B,DU H K.Numerical Range of the Aluthge Transform [J].Acta Analysis Functionalis Applicata,2005,7(3):193-197.
[13] JI G X,LIU N,LI Z.Essential Numerical Range and Maximal Numerical Range of the Aluthge Transform [J].Linear & Multilinear Algebra,2007,55(4):315-322.
[14] STAMPFLI J G.The Norm of a Derivation [J].Pacifi J Math,1970,33(3):737-747.
[15] ZHANG Y,JI G X.Spectral Properties of the Generalized Aluthge Transform [J].Acta Analysis Functionalis Applicata,2008,10(2):116-122.
[16] 刘秀梅,杨新兵.关于广义Aluthge变换的数值域 [J].纯粹数学与应用数学,2010,26(1):111-114.