SOME REFINEMENTS OF BEREZIN NUMBER INEQUALITIES VIA CONVEX FUNCTIONS
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.72, sa.1, ss.32-42, 2023 (ESCI, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 72 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.31801/cfsuasmas.1089790
- Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.32-42
- Anahtar Kelimeler: Berezin number, Berezin transform, Cauchy-Schwarz inequality, Young inequality, reproducing kernel Hilbert space, NUMERICAL RADIUS INEQUALITIES, HOLDER-MCCARTHY, OPERATORS, SYMBOLS, BOUNDS
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
The Berezin transform (A) over tilde and the Berezin number of an operator A on the reproducing kernel Hilbert space over some set Omega with normalized reproducing kernel (k) over cap (lambda) are defined, respectively, by (A) over tilde(lambda) = < A((k) over cap (lambda), (k) over cap (lambda)>, lambda is an element of Omega and ber(A) := sup(lambda is an element of Omega) |($) over tilde(lambda)|. A straightforward comparison between these characteristics yields the inequalities ber (A) <= 1/2 (||A||(ber) + ||A2||(1/2)(ber)). In this paper, we study further inequalities relating them. Namely, we obtained some refinements of Berezin number inequalities involving convex functions. In particular, for A is an element of B (H) and r >= 1 we show that