本性正规算子的Aluthge变换  

Aluthge transforms of essentially normal operators

作　　者：张云[1] 陈冬君[1] 

机构地区：[1]淮北煤炭师范学院数学科学学院,安徽淮北235000

出　　处：《山东大学学报（理学版）》2009年第3期88-91,共4页Journal of Shandong University(Natural Science)

基　　金：安徽省高校省级自然科学研究项目(2006KJ256B)

摘　　要：设T∈B(H),T=U|T|是算子T的极分解,则定义Tt～=|T|tU|T|1-t和T～t(*)=|T*|tU|T*|1-t(其中0<t<1)分别为算子的广义Aluthge变换和广义*-Aluthge变换。本文利用算子矩阵分块和算子逼近的技巧,研究了本性正规算子及其广义的Aluthge变换和广义的*-Aluthge变换三者之间的关系,得出广义的Aluthge变换和广义的*-Aluthge变换保持本性正规性。同时,根据BDF定理,进一步证明了它们三者之间是模紧酉等价的。Let T∈B（H）,T=U｜T｜ be a polar decomposition of Tt^-=｜T｜^tU｜T｜^1-t and Tt^-（＊）=｜T^＊｜^tU｜T^＊｜1-t were defined to be the generalized Aluthge transform and the generalized ＊ -Aluthge transform of T respectively, arbitary t∈ （0,1）. Using block operator matrices and operator approximation, the relationships among the generalized Aluthge transform, the genralized ＊ -Aluthge transform and the class of essentially Normal Operators were discussed. In this note, it was proved that both the generalized Aluthge transform and the generalized ＊ -Aluthge transform preserve essential normality. Moreover, it was shown that T,Tt^- and Tt^-（＊） are mutually essentially unitary equivalent.

关 键 词：广义ALUTHGE变换 广义＊-Aluthge变换 BDF定理 模紧酉等价 

分 类 号：O177.1[理学—数学]