On Two Natural Extensions of n-normality  

作　　者：Salah MECHERI 

机构地区：[1]Faculty of Mathematics and informatics,Mohamed El Bachir El Ibrahimi University,Bordj Bou Arreridj,Algeria

出　　处：《Acta Mathematica Sinica,English Series》2023年第6期1147-1152,共6页数学学报（英文版）

摘　　要：A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.

关 键 词：Normal operator n-normal operator invariant subspace 

分 类 号：O177[理学—数学]