ON GENERALIZED DAVIS-WIELANDT RADIUS INEQUALITIES OF SEMI-HILBERTIAN SPACE OPERATORS

Let A be a positive (semidefinite) operator on a complex Hilbert space H and let A = ((A O)(O A)). We obtain upper and lower bounds for the A-Davis-Wielandt radius of semiHilbertian space operators, which generalize and improve on the existing ones. Further, we derive upper bounds for the A-Davis-Wielandt radius of the sum of the product of semi-Hilbertian space operators. We also obtain upper bounds for the A-Davis-Wielandt radius of 2x2 operator matrices. Finally, we determine the exact value for the A-Davis-Wielandt radius of two operator matrices ((I X)(O O)) and ((O X)(O O)), where X is a semi-Hilbertian space operator, and I, O are the identity operator, the zero operator on H, respectively.