# On a new norm on B(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B}({\mathcal {H}})$$\end{document} and its applications to numerical radius inequalities

On a new norm on B(H)\documentclass[12pt]{minimal} \usepackage{amsmath}... We introduce a new norm on the space of all bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis–Wielandt radius norm. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate that our results improve on some of the important existing numerical radius inequalities. Other application of this new norm have also studied. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Functional Analysis Springer Journals

# On a new norm on B(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B}({\mathcal {H}})$$\end{document} and its applications to numerical radius inequalities

, Volume 12 (4) – Jul 20, 2021
25 pages

/lp/springer-journals/on-a-new-norm-on-b-h-documentclass-12pt-minimal-usepackage-amsmath-WxW29WN8Se
Publisher
Springer Journals
Copyright © Tusi Mathematical Research Group (TMRG) 2021
ISSN
2639-7390
eISSN
2008-8752
DOI
10.1007/s43034-021-00138-5
Publisher site
See Article on Publisher Site

### Abstract

We introduce a new norm on the space of all bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis–Wielandt radius norm. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate that our results improve on some of the important existing numerical radius inequalities. Other application of this new norm have also studied.

### Journal

Annals of Functional AnalysisSpringer Journals

Published: Jul 20, 2021

Keywords: Numerical radius; Bounded linear operator; Inequalities; Hilbert space; 47A30; 47A12; 47A63