New A-numerical Radius Equalities and Inequalities for Certain Operator Matrices and Applications

The main goal of this article is to establish several new A-numerical radius equalities for nxn circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where A is the nxn diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our results lead to the results of earlier works in the literature, which shows that our results are more general. Further, some pinching type A-numerical radius inequalities for nxn block operator matrices are given. Some equality conditions are also given. We also provide a concluding section, which may lead to several new problems in this area.