On [Formula: see text] -numerical radius equalities and inequalities for certain operator matrices

The main goal of this article is to establish several new [Formula: see text] -numerical radius equalities for [Formula: see text] circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where [Formula: see text] is the [Formula: see text] 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 [Formula: see text] -numerical radius inequalities for [Formula: see text] 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.