Quadratic Numerical Radius Inequalities Of Block Operator Matrices

In this paper,the quadratic numerical radius of bounded block operator matrix is studied.First,several properties of quadratic numerical radius of special block operator matrices are obtained.Next,some quadratic numerical radius inequalities of off-diagonal block operator matrices and general block operator matrices are studied.In addition,the Pinching inequalities of quadratic numerical radius are obtained under some conditions,and use it to give new quadratic numerical radius inequalities of block operator matrices.