Improvements of some Berezin radius inequalities

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GÜRDAL M., Alomari M. W.

Constructive Mathematical Analysis, cilt.5, sa.3, ss.141-153, 2022 (Scopus, TRDizin)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 5 Sayı: 3
• Basım Tarihi: 2022
• Doi Numarası: 10.33205/cma.1110550
• Dergi Adı: Constructive Mathematical Analysis
• Derginin Tarandığı İndeksler: Scopus, TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.141-153
• Anahtar Kelimeler: Berezin radius, Furuta inequality, Mixed Schwarz inequality
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Süleyman Demirel Üniversitesi Adresli: Evet

Özet

© 2022 Himia, Fizika ta Tehnologia Poverhni. All rights reserved.The Berezin transform Ae and the Berezin radius of an operator A on the reproducing kernel Hilbert space over some set Qwith normalized reproducing kernel kη := kKKηηk are defined, respectively, by Ae(η) = hAkη, kηi, η ∈ Qand ber(A):= supη∈Q|||Ae(η) |||. A simple comparison of these properties produces the inequalities 14 kA∗A + AA∗k ≤ ber2 (A) ≤ 21 kA∗A + AA∗k. In this research, we investigate other inequalities that are related to them. In particular, for A ∈ L(H(Q)) we prove that ber2 (A) ≤ 12 kA∗A + AA∗kber − 14 ηinf ∈Q ((|fA|(η)) − (|gA∗|(η) ))2