On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

Abstract

The main goal of this article is to establish several new -numerical radius equalities for n × n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where is the n × n 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 -numerical radius inequalities for n × n 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.

Generalized $A$-numerical radius of operators and related inequalities

“…Several results on the A-numerical radius have been established by many mathematicians, (see [6,8,12,13,14,20,22] and the references therein). ω A (•) defines a seminorm on B A 1/2 (H) which is equivalent to the A-operator seminorm • A .…”