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 (β) , A is decomposable and the quasi-nilpotent part H 0 (A − λ) of A satisfies H 0 (A − λ) −1 (0) = (A − λ) −1 (0) for every non-zero complex λ. 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.