<abstract xmlns="http://www.w3.org/1999/xhtml">

We study the numerical radius of bounded operators on direct sum of a family of Hilbert spaces with respect to the ℓ<italic>p</italic>-norm, where 1 ≤ <italic>p</italic> ≤∞. 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 ℓ<italic>p</italic>-norm, where 1 ≤ <italic>p</italic> ≤ 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 ℓ<italic>p</italic>-sum of Hilbert spaces where 2 <italic>&lt;p &lt;</italic> ∞. We also present some applications of our results.
</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 <p < ∞. We also present some applications of our results.

Numerical Radius of Bounded Operators with ℓ<italic>p</italic>-Norm

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Numerical Radius of Bounded Operators with ℓ-Norm

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...

Numerical Radius of Bounded Operators with ℓ^p-Norm

Published Online: Nov 29, 2022

Page range: 155 - 164

Received: Aug 28, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0012

Keywords
numerical radius, inner product, ℓ-sum

© 2022 Sadaf Fakri Moghaddam et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Numerical Radius of Bounded Operators with ℓp-Norm

Published Online: Nov 29, 2022

Page range: 155 - 164

Received: Aug 28, 2021

DOI: https://doi.org/10.2478/tmmp-2022-0012

Keywordsnumerical radius, inner product, ℓ-sum

© 2022 Sadaf Fakri Moghaddam et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Numerical Radius of Bounded Operators with ℓ^p-Norm

Keywords
numerical radius, inner product, ℓ-sum