Q-Numerical radius inequalities for Hilbert space

Abstract

The aim of this paper is to study the q-numerical radius ω q ( . ) of bounded linear operators on Hilbert spaces. More precisely, first, we show that ω q ( . ) defines a norm which is equivalent to the operator norm. Next, the following compatible generalization of Kittaneh's inequality 1 4 ( q 2 − q 2 ) 2 ∥ T ∗ T + T T ∗ ∥ ≤ ω q 2 ( T ) ≤ ( q + 2 1 − q 2 ) 2 2 × ‖ T ∗ T + T T ∗ ‖ . is obtained. Finally, some generalizations of q-numerical radius inequalities for composition of operators are established.