Abstract
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let 9L be a Hilbert space and let A be a positive bounded operator on 9L. The semi -inner product < h vertical bar k > A := < Ah vertical bar k >, h, k is an element of H, induces a semi-norm parallel to.parallel to(A). This makes 9L into a semi-Hilbertian space. An operator T is an element of B-A(H) is said to be (n, m) -A-normal if [T-n, (T(#)A)(m)] := T-n(T(#)A)(m) - (T(#)A)T-m(n) = 0 for some positive integers n and m.