A-Numerical Radius And A-Norm Inequalities For Semi-Hilbertian Space Operators

Let (H, <., .>) be a complex Hilbert space and A be a positive bounded linear operator on H. The semi-inner product < x, y >(A) := < Ax, y >, x, y is an element of H, induces a semi-norm parallel to . parallel to(A) on H. Let omega(A)(T) and parallel to T parallel to(A) denote the A-numerical radius and the A-operator semi-norm of an operator T in semi-Hilbertian space (H, <., .>(A)), respectively. In this paper, some new bounds for the A-numerical radius of operators in semi-Hilbertian space are obtained, which improve the existing ones. In particular, a refinement of the triangle inequality for A-operator semi-norm is also shown.