ON THE ESTIMATION OF q–NUMERICAL RADIUS OF HILBERT SPACE OPERATORS

Abstract

The objective of this article is to estimate the q-numerical radius of bounded linear operators on complex Hilbert spaces. One of our main results states that for a bounded linear operator T in a Hilbert space H and q ∈ [0,1], the relation (Formula Presented) holds where w(T), w<inf>q</inf> (T) are the numerical radius and q-numerical radius of T respectively. Several refined new upper bounds follow from this result. Finally, the q-numerical radius of 2 × 2 operator matrices is explored and several new results are established. © 2024, Element D.O.O.. All rights reserved.