On nth roots of normal operators

Abstract

For n-normal operators A [2,4,5], equivalently n-th roots A of normal Hilbert space operators, both A and A* satisfy the Bishop-Eschmeier-Putinar property (?)?, A is decomposable and the quasinilpotent part H0(A-?) of A satisfies H0(A-?=)-1(0) = (A-?)-1(0) for every non-zero complex ?. A satisfies every Weyl and Browder type theorem, and a sufficient condition for A to be normal is that either A is dominant or A is a class A(1,1) operator.