Integral Numerical Radius and Operator Matrix Bounds
Shiva Sheybani, Hamid Reza Moradi, and Mohammad Sababheh
TL;DR
This paper introduces new integral inequalities that improve bounds on the numerical radius and operator norm of bounded linear operators, using convex combinations and averaging techniques to reveal deeper structural insights.
Contribution
It presents novel integral inequalities that refine classical bounds and establish new identities and equality conditions for the numerical radius and operator norm.
Findings
Sharper bounds for numerical radius and operator norm
New identities and equality conditions
Deeper structural connections uncovered
Abstract
We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex combinations and integral averaging techniques. Several consequences, including new identities, sharper bounds, and equality conditions, are obtained, revealing deeper structural connections between the numerical radius and operator norm.
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Taxonomy
TopicsMathematical Inequalities and Applications · Optimization and Variational Analysis · Matrix Theory and Algorithms