ON THE δ-NUMERICAL RADIUS AND THE δ-CRAWFORD NUMBER FUNCTIONS OF DIRECT SUM OF HILBERT SPACE OPERATORS
JOURNAL OF MATHEMATICAL INEQUALITIES, cilt.20, sa.1, ss.121-145, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.7153/jmi-2026-20-09
- Dergi Adı: JOURNAL OF MATHEMATICAL INEQUALITIES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.121-145
- Karadeniz Teknik Üniversitesi Adresli: Hayır
Özet
In this work, some important properties of the 8-numerical radius and the 8-Crawford number functions of bounded linear operators on Hilbert spaces are investigated. Then, the relationships between the 8-numerical radius and the 8-Crawford number functions of the direct sum of Hilbert space operators and those of their coordinate operators are explored. Furthermore, some generalization formulas for lower and upper bounds of the 8-numerical radius and the 8-Crawford number functions of such direct sums are obtained. Finally, some lower and upper bounds for the 8-numerical radius in the sectorial cases of coordinate operators are established, and these evaluations generalize some results known in the literature. Moreover, the obtained results offer a range of useful techniques that can facilitate further advancements in this field.