关键词: BDF定理, 模紧酉等价, 广义Aluthge变换, 广义*Aluthge变换

Abstract: Let T∈B(H), T=U|T| be a polar decomposition of T, then 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,　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.

Key words: the generalized Aluthge transform, the genralized *Aluthge transform, BDF theorem, compalent