ON n-POWER NORMAL OPERATORS

摘要

We introduce the class of n-power normal operators, and prove that an operator T ∈ L(H) is n-power normal if and only if T~n is normal; if and only if ‖T~nx‖ = ‖(T~n)~*(x)‖ for all x ∈ H. We give some properties of these operators in general, and also study the special case when an operator is n-power normal for n = 2, 3.