IMPROVING BOUNDS FOR GENERALIZED BEREZIN NUMBER OF OPERATORS
Proceedings of the Institute of Mathematics and Mechanics, vol.51, no.2, pp.171-191, 2025 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 51 Issue: 2
- Publication Date: 2025
- Doi Number: 10.30546/2409-4994.2025.51.2.4090
- Journal Name: Proceedings of the Institute of Mathematics and Mechanics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.171-191
- Keywords: A-Berezin number, A-operator semi-norm, Reproducing kernel Hilbert space
- Süleyman Demirel University Affiliated: Yes
Abstract
This paper introduces an improvement of the Cauchy-Schwarz inequality in a semi-Hilbertian space with the inner product induced by an A-positive operator. This improved A-Cauchy-Schwarz inequality is then used to improve the bounds of the A-Berezin number of operators. First, we present upper bounds for the A-Berezin number of the product of two operators. Then, A-Berezin number bounds for the sum of two operators are developed. This work refines and extends some of the A-Berezin inequalities previously established in the literature.