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Integral Numerical Radius and Operator Matrix Bounds

Shiva Sheybani, Hamid Reza Moradi, Mohammad Sababheh

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.

Integral Numerical Radius and Operator Matrix Bounds

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.
Paper Structure (2 sections, 11 theorems, 47 equations)

This paper contains 2 sections, 11 theorems, 47 equations.

Table of Contents

  1. Introduction
  2. Main results

Key Result

Theorem 2.1

Let $A,B\in \mathbb B\left( \mathbb H \right)$. Then

Theorems & Definitions (21)

  • Theorem 2.1
  • proof
  • Corollary 2.1
  • proof
  • Theorem 2.2
  • proof
  • Corollary 2.2
  • proof
  • Corollary 2.3
  • proof
  • ...and 11 more