Some properties of the q-numerical radius

Abstract

In the given study, we consider the q-numerical radius (Formula presented.) of operator matrices defined on a direct sum of Hilbert spaces and investigate the various inequalities involving these values. We also prove that (Formula presented.) for all the (Formula presented.), thereby extending the well known equality regarding the numerical radii that occurs when we plug in q = 1. Subsequently, we give explicit formulae for computing (Formula presented.) for some special cases of operator matrices. Finally, we establish some analytical properties of (Formula presented.) regarded as a function in q.