Numerical radius of bounded operators with $\ell^p$-norm

Year, pages: 2022, 155 - 164

We study the numerical radius of bounded operators on direct sum of a family of Hilbert spaces with respect to the $\ell^p$-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 $\ell^p$-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 $\ell^p$-sum of Hilbert spaces where $2≤ p ≤ ∞$. We also present some applications of our results.

Moghaddam, S., Mirmostafaee, A. 2022. Numerical radius of bounded operators with $\ell^p$-norm. In Tatra Mountains Mathematical Publications, vol. 81, no.1, pp. 155-164. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0012

Moghaddam, S., Mirmostafaee, A. (2022). Numerical radius of bounded operators with $\ell^p$-norm. Tatra Mountains Mathematical Publications, 81(1), 155-164. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2022-0012

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/