On powers of class A(k) operators including p-hyponormal and log-hyponormal operators

Abstract

In [11], we introduced class A( k ) as a class of operators including p -hyponormal and log -hyponormal operators. In this paper, we shall show that “if T is an invertible class A( k ) operator for k ∈ (0, 1] , then Tn is a class A( k n ) operator for all positive integer n .” Moreover, we shall show a similar result on powers of class AI( s, t ) operators which were introduced in [7] as extensions of class A( k ) operators, that is, “if T is a class AI( s, t ) operator for s, t ∈ (0, 1] , then Tn is a class AI( s n , t n ) operator for all positive integer n .” Mathematics subject classification (1991): 47B20, 47A63.