Year 2021, Volume 50 , Issue 3, Pages 795 - 810 2021-06-07

Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices

Kais FEKİ [1]


For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle_A \big)$ where ${\langle x, y\rangle}_A := \langle Ax, y\rangle$ for every $x, y\in\mathcal{H}$. The $A$-numerical radius of an $A$-bounded operator $T$ on $\mathcal{H}$ is given by
\[\omega_A(T)=\sup\Big\{\big|{\langle Tx, x\rangle}_A\big|\,;\,\, x\in\mathcal{H},\, {\langle x, x\rangle}_A=1\Big\}.\]
Our aim in this paper is to derive several $\mathbb{A}$-numerical radius inequalities for $2\times 2$ operator matrices whose entries are $A$-bounded operators, where $\mathbb{A}=\text{diag}(A,A)$.
positive operator, operator matrix, semi-inner product, $A$-numerical radius, inequality
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-9326-4173
Author: Kais FEKİ (Primary Author)
Institution: University of Sfax
Country: Tunisia


Dates

Publication Date : June 7, 2021

Bibtex @research article { hujms730574, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2021}, volume = {50}, pages = {795 - 810}, doi = {10.15672/hujms.730574}, title = {Some bounds for the \$\\mathbb\{A\}\$-numerical radius of certain \$2 \\times 2\$ operator matrices}, key = {cite}, author = {Feki, Kais} }
APA Feki, K . (2021). Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices . Hacettepe Journal of Mathematics and Statistics , 50 (3) , 795-810 . DOI: 10.15672/hujms.730574
MLA Feki, K . "Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices" . Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 795-810 <https://dergipark.org.tr/en/pub/hujms/issue/62731/730574>
Chicago Feki, K . "Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices". Hacettepe Journal of Mathematics and Statistics 50 (2021 ): 795-810
RIS TY - JOUR T1 - Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices AU - Kais Feki Y1 - 2021 PY - 2021 N1 - doi: 10.15672/hujms.730574 DO - 10.15672/hujms.730574 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 795 EP - 810 VL - 50 IS - 3 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.730574 UR - https://doi.org/10.15672/hujms.730574 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices %A Kais Feki %T Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices %D 2021 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 50 %N 3 %R doi: 10.15672/hujms.730574 %U 10.15672/hujms.730574
ISNAD Feki, Kais . "Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices". Hacettepe Journal of Mathematics and Statistics 50 / 3 (June 2021): 795-810 . https://doi.org/10.15672/hujms.730574
AMA Feki K . Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 795-810.
Vancouver Feki K . Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices. Hacettepe Journal of Mathematics and Statistics. 2021; 50(3): 795-810.
IEEE K. Feki , "Some bounds for the $\mathbb{A}$-numerical radius of certain $2 \times 2$ operator matrices", Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 3, pp. 795-810, Jun. 2021, doi:10.15672/hujms.730574