Conference Paper
Year 2024,
Volume: 28, 375 - 381, 01.08.2024
Abstract
References
- 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.
Year 2024,
Volume: 28, 375 - 381, 01.08.2024
Abstract
We present a collection upper bounds for the numerical radii of a certain 2 Γ 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 π΄ is a bounded linear operator on a complex Hilbert space, then π€ 2π (π΄) β€ 1+πΌ 8 β|π΄| 2π +|π΄ β | 2πβ+ 1+πΌ 4 π€(|π΄| π |π΄ β | π )+ 1βπΌ 2 π€ π (π΄ 2 ) for every r β₯ 1 and Ξ± β [0,1]. This substantially improves on the existing inequality π€ 2π (π΄) β€ 1 2 β|π΄| 2π + |π΄ β | 2πβ. Here π€(. ) and ||. || denote the numerical radius and the usual operator norm, respectively.
References
- 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.
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Details
| Primary Language | English |
|---|---|
| Subjects | Software Engineering (Other) |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | July 29, 2024 |
| Publication Date | August 1, 2024 |
| Submission Date | February 7, 2024 |
| Acceptance Date | April 22, 2024 |
| Published in Issue | Year 2024Volume: 28 |
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