q -Numerical radius inequalities for Hilbert space

New upper bounds for the numerical radius of Hilbert space operators

“…This shows that the inequality mentioned in (11) provides an improvement on the result (6), proved in Theorem 2.10 in [12].…”

“…Here we prove the refinement of the above result in comparison to the existing upper bound (7) of ω 2 (T ) mentioned in Theorem 3.1 in [12]. For this, we use the fact that…”

“…Our interest in this paper lies in the direction of obtaining refined q-numerical radius inequalities. In section 2 we established upper bounds for q-numerical radius that generalize the results of [12]. In addition, the q-numerical radius bounds for 2 × 2 operator matrices are also discussed in section 3.…”

“…Lemma 2.2. [12] The q-numerical radius defines a semi-norm on B(H). The number m(T ) is known as the transcendental radius of T .…”

“…Duan [11] draws attention to the vital significance that the idea of q-numerical range plays in characterizing the perfect distinguishability of quantum operations. Recently, Moghaddam et al [12] have studied several q-numerical radius bounds. The following are a few of the inequalities they have derived.…”