TY  - JOUR
T1  - General Upper Bounds for the Numerical Radii of Hilbert Space Operators
AU  - Al- Dolat, Mohammed
PY  - 2024
DA  - August
Y2  - 2024
DO  - 10.55549/epstem.1523566
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 375
EP  - 381
VL  - 28
LA  - en
AB  - 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.
KW  - Numerical radius
KW  - Usual operator norm
KW  - Operator matrix
KW  - Buzano
KW  - s inequality.
CR  - 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.
UR  - https://doi.org/10.55549/epstem.1523566
L1  - https://dergipark.org.tr/en/download/article-file/4103072
ER  -