Spectral estimates for multiparametric operator products via the A-Berezin norm in RKHSs
AIMS Mathematics, cilt.11, sa.3, ss.6217-6230, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 11 Sayı: 3
- Basım Tarihi: 2026
- Doi Numarası: 10.3934/math.2026256
- Dergi Adı: AIMS Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
- Sayfa Sayıları: ss.6217-6230
- Anahtar Kelimeler: A-Berezin number, Berezin number, multiparametric inequalities, reproducing kernel Hilbert space, Schatten-type exponents, semi-inner product
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper addresses the spectral analysis of operators acting on reproducing kernel Hilbert spaces equipped with a semi-inner product induced by a positive operator A. A fundamental challenge in this setting is the geometric discrepancy between the normalized reproducing kernels and the unit A-sphere, which renders classical numerical radius techniques inapplicable. By overcoming this structural obstacle, we establish sharp inequalities for the A-Berezin number and A-Berezin norm. Our main contribution involves the derivation of multiparametric estimates for triple operator products of the form PαXRα involving Schatten-type exponents. These results generalize and refine existing bounds in the literature. Furthermore, we provide a qualitative analysis of the obtained bounds through weighted Toeplitz operators on Hardy spaces and verify the theoretical findings with concrete matrix examples involving the geometric behavior of weight functions.