Advanced refinements of Berezin number inequalities
Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, cilt.72, sa.2, ss.386-396, 2023 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 72 Sayı: 2
- Basım Tarihi: 2023
- Doi Numarası: 10.31801/cfsuasmas.1160606
- Dergi Adı: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.386-396
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
For a bounded linear operator $A$ on a functional Hilbert space $mathcal{H}left( Omegaright) $, with normalized reproducing kernel $widehat {k}_{eta}:=frac{k_{eta}}{leftVert k_{eta}rightVert _{mathcal{H}}},$ the Berezin symbol and Berezin number are defined respectively by $widetilde{A}left( etaright) :=leftlangle Awidehat{k}_{eta},widehat{k}_{eta}rightrangle _{mathcal{H}}$ and $mathrm{ber}(A):=sup_{etainOmega}leftvert widetilde{A}{(eta)}rightvert .$ A simple comparison of these properties produces the inequality $mathrm{ber}% left( Aright) leqfrac{1}{2}left( leftVert ArightVert_{mathrm{ber}}+leftVert A^{2}rightVert _{mathrm{ber}}^{1/2}right) $ (see [17]). In this paper, we prove further inequalities relating them, and also establish some inequalities for the Berezin number of operators on functional Hilbert spaces