q-Numerical radius inequalities for Hilbert space
Sadaf Fakhri Moghaddam, Alireza Kamel Mirmostafaee, Mohammad Janfada · Linear and Multilinear Algebra · 2023
The aim of this paper is to study the q-numerical radius ωq(.) of bounded linear operators on Hilbert spaces. More precisely, first, we show that ωq(.) defines a norm which is equivalent to the operator norm. Next, the following compatible generalization of Kittaneh's inequality 14(q2−q2)2∥T∗T+TT∗∥≤ωq2(T)≤(q+21−q2)22×‖T∗T+TT∗‖.is obtained. Finally, some generalizations of q-numerical radius inequalities for composition of operators are established.