Refined inequalities for the (Formula presented.)-Berezin radii of operators on reproducing kernel Hilbert spaces
International Journal of Mathematics, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0129167x26500837
- Dergi Adı: International Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, DIALNET, Academic Search Ultimate (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: (Formula presented.)-Berezin radius, Berezin number, Buzano inequality, operator matrices, reproducing kernel Hilbert space
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
Let (Formula presented) be a reproducing kernel Hilbert space, fix (Formula presented), and assume that its normalized kernel family contains pairs with inner product (Formula presented). We obtain upper bounds for the (Formula presented)-Berezin radius in terms of the Berezin number and (Formula presented), where (Formula presented) denotes the kernel norm. Applying Buzano’s inequality and a Gram determinant inequality to (Formula presented) and (Formula presented) gives further bounds involving (Formula presented) and (Formula presented), with (Formula presented). We also obtain inequalities for (Formula presented) operator matrices using numerical-radius estimates and a specified family of normalized kernels. Applications include operator products and commutators. A finite-dimensional example compares the bounds with an earlier estimate. A finite-rank operator on the Hardy space gives equality in the Buzano bound at (Formula presented).