Improved Berezin radius inequalities for functional Hilbert space operators
Turkish Journal of Mathematics, cilt.49, sa.5, ss.545-561, 2025 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 49 Sayı: 5
- Basım Tarihi: 2025
- Doi Numarası: 10.55730/1300-0098.3607
- Dergi Adı: Turkish Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.545-561
- Anahtar Kelimeler: 47A63, Berezin number, berezin symbol, furuta’s inequality
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
The Berezin number of an operator S is defined by ber(S) = sup sup|S(λ)|λ∈R= sup|(Skλ, kλ)|, where S(λ) = (Skλ, kλ) (λ ∈ θ) is the Berezin transform of an operator S on the functional Hilbert space H = H (θ) and kλ = kλ ∥kλ ∥ is the normalized reproducing kernel of H. In this paper, we show an improvement of the classical Cauchy*Schwarz inequality involving the Berezin number. Moreover, some Berezin numbers inequalities are proven for invertible operators.