The Inequalities For The Essential Numerical Radius Of 2×2 Block Operator Matrices

Let A=(?)be a bounded linear operator on complex separable Hilbert space.In this paper,the range for the essential numerical range of a special kind of 2×2 block operator matrix and the essential numerical radius of usual 2×2 block operator matrix was studied.Firstly,when operators B and C are compact,it is obtained that the essential numerical range of A satisfies We(A)=Conv(We(A)U We(D)).secondly,we consider the equivalent seminorm of the essential numerical radius.Finally,we describe the range for essential numerical radius of usual 2 × 2 block operator matrices by the essential numerical radius of operators A and D.