Further q-Berezin Radius Inequalities on Reproducing Kernel Hilbert Spaces
Complex Analysis and Operator Theory, cilt.20, sa.7, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s11785-026-02025-0
- Dergi Adı: Complex Analysis and Operator Theory
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Inequality, Numerical radius, Operator norm
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
We develop several new inequalities for the q-Berezin radii of bounded linear operators on reproducing kernel Hilbert spaces. Our first purpose is to provide a corrected and fully rigorous proof of a previously stated estimate for the q-Berezin radii of operator sums. Building on that correction, we then establish product-type estimates for operators of the form AαXBβ, prove a Heinz-type inequality in the q-Berezin setting, and derive a lower bound for the q-Berezin radius in terms of the Berezin norm of T∗T+TT∗. These results sharpen and extend earlier estimates in the literature, while highlighting the geometric role played by the parameter q and the reproducing-kernel structure of the underlying Hilbert space.