Some spectral properties and convergence of the (A,q)-numerical radius and (A,q)-Crawford number

2025/05/22 by Pembe İpek Al, Zameddin I. İsmailov, Al, Pembe Ipek +5
Mathematics · #47A05 #47A12 #47A30 #47A63 #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2505.16924

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study, some estimates are given for the (A,q)-numerical radius and (A,q)-Crawford number via the A-numerical radius and A-Crawford number for the A -bounded linear operators in any complex semi-Hilbert space, respectively. Then, some evolutions are studied for the tensor product of two operators. Lastly, some convergence properties of the (A,q)-numerical radius and (A,q)-Crawford number, via the A-uniform convergence of operator sequences, are investigated. We also considered several examples to illustrate our results. Finally, a few applications of some operator functions classes are also given.

Citations

• Weighted Inequalities For The Numerical Radius
• Numerical radius inequalities for products and sums of semi-Hilbertian space operators
• Some refinements of numerical radius inequalities
• A-numerical radius inequalities for semi-Hilbertian space operators
• Numerical radius inequalities for Hilbert Space Operators
• Operator Hölder--Zygmund functions

Related

• On numerical radius and Crawford number attainment sets of a bounded linear operator
• On the A-q-Numerical Range of Operators in Semi-Hilbertian Spaces
• A-numerical radius and product of semi-Hilbertian operators
• Certain Upper Bounds on the A-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
• New upper bounds for the q-numerical radius of Hilbert space operators