Numerical radius and norm inequalities via a Cauchy-Schwarz extension
Abstract
Abstract The generalization of inequalities involving the numerical radius is a well-established topic in functional analysis. In this article, we present refinements to certain known generalizations by employing an extension of the Cauchy–Schwarz inequality formulated in terms of the angle between two vectors. Let T i , S i , R i ∈ B ( K ) ${T}_{i},{S}_{i},{R}_{i}\in \mathcal{B}(\mathcal{K})$ , where R i ’s have the polar decomposition R i = V i | R i | for i = 1, 2, …, n . Suppose that ϕ and ψ are non-negative functions satisfying ϕ ( s ) ψ ( s ) = s , ( s ≥ 0). It is shown that, if either 0 ≤ θ i < θ R i , T i x , S i x ≤ π 2 $0\le {\theta }_{i}< {\theta }_{{R}_{i},{T}_{i}x,{S}_{i}x}\le \frac{\pi }{2}$ for all unit vectors x ∈ K $x\in \mathcal{K}$ or π 2 ≤ θ R i , T i x , S i x < θ i
Fields of Study & Subjects
Mathematical Inequalities and Applications
Functional Equations Stability Results
Mathematical functions and polynomials
Publication details
- Journal / source
- Mathematica Slovaca
- Publisher
- Walter de Gruyter GmbH
- Volume
- 76
- Issue
- 3
- Pages
- 795–810
- Publication date
- 22 April 2026
- Language
- EN