Refined q-Berezin Radius Inequalities for Operators and 2×2 Block Matrices
Complex Analysis and Operator Theory, vol.20, no.4, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 20 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1007/s11785-026-01951-3
- Journal Name: Complex Analysis and Operator Theory
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Keywords: Berezin norm, Berezin number, Operator matrix inequality, q-Berezin radius, Reproducing kernel Hilbert space
- Süleyman Demirel University Affiliated: Yes
Abstract
In this paper, we establish upper bounds for the q-Berezin radii of bounded linear operators acting on reproducing kernel Hilbert spaces. Specifically, we derive inequalities for the sum X+Y and product Y∗X of operators utilizing the Berezin norms of operator powers and integral refinements of the Cauchy-Schwarz inequality. We further provide explicit estimates for the q-Berezin radii of 2×2 block operator matrices bounding the off-diagonal terms in relation to the diagonal entries. The obtained results recover the standard Berezin number inequalities when q=1 and provide stronger estimates than the existing upper bounds for the general q-numerical radius.