On A-Berezin number in functional Hilbert space
Filomat, vol.38, no.21, pp.7657-7671, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 38 Issue: 21
- Publication Date: 2024
- Doi Number: 10.2298/fil2421657g
- Journal Name: Filomat
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.7657-7671
- Keywords: A-Berezin norm, A-Berezin norm distance, A-Berezin number, A-Berezin radius distance, functional Hilbert space, inequality, positive operator
- Süleyman Demirel University Affiliated: Yes
Abstract
A-Berezin radius distance and A-Berezin norm distance are presented in this study. Furthermore, by employing the notions of A-Berezin radius distance and A-Berezin norm distance, we find A-Berezin radius inequalities of the product and commutator of functional Hilbert space operators. Moreover, we generalize the A-Berezin radius distance. Finally, we prove the theorem pertaining to the A-Berezin radius distance. To recapitulate, the A-Berezin number∣ of operator V on L (H(Θ)) is defined by the following ∣∣∣〈 〉 special type of quadratic form: berA (V) = supη∈ΘV̂kη,̂kη ∣ ∣, η ∈ Θ, whereˆkη is the normalized reproducing kernel on H and a semi-inner product on H, denoted as ⟨Vˆkη,ˆkη ⟩A:= ⟨AVˆkη,ˆkη ⟩H, is induced by any positive operator A. A.