算子集上的伪双曲距离

算子集上的伪双曲距离 Pseudo Hyperbolic Distance in Operator Set 吴树宏 WU Shu-hong~1 1 2 3 first-author 左红亮 ZUO Hong-liang~2 1 2 3 华中科技大学数学系 华中科技大学数学系 Department of Mathematics, Huazhong University of Science and Technology Department of Mathematics, Huazhong University of Science and Technology 武汉大学数学与统计学院,湖北,武汉,430074 武汉大学数学与统计学院,湖北,武汉,430074 School of Mathematics and Stastistics, Wuhan University School of Mathematics and Stastistics, Wuhan University ,湖北,武汉,430072 ,湖北,武汉,430072 在复Hilbert空间上的有界线性算子构成的复Banach空间上,对算子范数小于1的交换自伴算子集定义了伪双曲距离,并且利用算子函数论的方法,证明了在此集合上定义的伪双曲距离满足距离公理且它关于变换φS（·）不变（此处S∈BH）. First we define pseudo hyperbolic distance in the set of selfadjoint and commuting operators in the complex Banach space composed by bounded linear operator in complex Hilbert space whose norm are less than 1, then prove pseudo hyperbolic distance meet the condition of axiom of distance and it is not change about transformation φ < sub > S（·） （where S∈B < sub > H） by means of operator function theory. 伪双曲距离 算子 距离公理 Key words: pseudo hyperbolic distance operator axiom of distance O177 华中科技大学博士后科研专项基金资助 2004-01-01 2021-04-01 1