Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if is a bounded linear operator on a complex Hilbert space, then
where , and are the operator norm, the numerical radius and the Crawford number, respectively. Further, we prove that if are bounded linear operators on a complex Hilbert space, then
where and . This is a refinement of a well-known inequality obtained by Bhatia and Kittaneh.
"Refinements of norm and numerical radius inequalities." Rocky Mountain J. Math. 51 (6) 1953 - 1965, December 2021. https://doi.org/10.1216/rmj.2021.51.1953