Numerical Radius Estimation Of Bounded Block Operator Matrices

In this paper,the numerical radius of bounded block operator matrices on Hilbert space is studied.Firstly,the generalized form of numerical radius inequalities of off-diagonal block operator matrix is studied,and take advantage of the unitary similarity invariance of numerical radius and the generalized mixed Schwarz inequality,the inequali-ties of the numerical radius of sum of two bounded linear operators are considered.Then,numerical radius inequalities for 2×2 bounded block operator matrices are given.Finally,the conclusion is applied in the bounded infinite dimensional Hamiltonian operator and the inequalities of its numerical radius are obtained.