Further Inequalities for the Numerical Radius of Hilbert Space Operators

2019/07/13 by Sara Tafazoli, Hamid Reza Moradi, Tafazoli, S. +4
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.1907.06003

openalex publication_date 2019/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if A∈ \mathbbB( H ) and r≥ 2, then w^r( A )≤ ‖ A ‖^r-\underset‖ x ‖=1\mathopinf ‖ | | A |-w( A ) |^(r)/(2)x ‖² where w( ⋅ ) and ‖ ⋅ ‖ denote the numerical radius and usual operator norm, respectively.

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