Abstract
Let H be a Hilbert space and let A be a positive bounded operator on H. The semi-inner product < u vertical bar v > A := < Au vertical bar v > , u, v is an element of H induces a semi-norm parallel to.parallel to(A) on H. This makes H into a semi-Hilbertian space. In this paper, we introduce a new class of operators called (alpha, ss)-A-normal operators in semi-Hilbertian spaces. Some structural properties of this class of operators are established.