Öz
Kaynakça
- Al-Dolat, M. (2024). General upper bounds for the numerical radii of Hilbert space operators The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 375-381.
Öz
We present a collection upper bounds for the numerical radii of a certain 2 × 2 operator matrices. We use these bounds to improve on some known numerical radius inequalities for powers of Hilbert space operators. In particular, we show that if 𝐴 is a bounded linear operator on a complex Hilbert space, then 𝑤 2𝑟 (𝐴) ≤ 1+𝛼 8 ‖|𝐴| 2𝑟 +|𝐴 ∗ | 2𝑟‖+ 1+𝛼 4 𝑤(|𝐴| 𝑟 |𝐴 ∗ | 𝑟 )+ 1−𝛼 2 𝑤 𝑟 (𝐴 2 ) for every r ≥ 1 and α ∈ [0,1]. This substantially improves on the existing inequality 𝑤 2𝑟 (𝐴) ≤ 1 2 ‖|𝐴| 2𝑟 + |𝐴 ∗ | 2𝑟‖. Here 𝑤(. ) and ||. || denote the numerical radius and the usual operator norm, respectively.
Anahtar Kelimeler
Numerical radius Usual operator norm Operator matrix Buzano s inequality.
Kaynakça
- Al-Dolat, M. (2024). General upper bounds for the numerical radii of Hilbert space operators The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 28, 375-381.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Yazılım Mühendisliği (Diğer) |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 29 Temmuz 2024 |
| Yayımlanma Tarihi | 1 Ağustos 2024 |
| Gönderilme Tarihi | 7 Şubat 2024 |
| Kabul Tarihi | 22 Nisan 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 28 |
