Numerical Radius of Bounded Operators with ℓp-Norm

Abstract We study the numerical radius of bounded operators on direct sum of a family of Hilbert spaces with respect to the ℓp-norm, where 1 ≤ p ≤∞. We propose a new method which enables us to prove validity of many inequalities on numerical radius of bounded operators on Hilbert spaces when the underling space is a direct sum of Hilbert spaces with ℓp-norm, where 1 ≤ p ≤ 2. We also provide an example to show that some known results on numerical radius are not true for a space that is the set of bounded operators on ℓp-sum of Hilbert spaces where 2