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Volume 58, Issue 3
Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application

Muqile Gao, Deyu Wu & Alatancang Chen

DOI: 10.4208/jms.v58n3.25.05

J. Math. Study, 58 (2025), pp. 323-337.

Published online: 2025-09

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  • Abstract

We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds. Moreover, the conclusion is applied to the non-monic operator polynomials and gives a new bound for the eigenvalues of these operator polynomials.

  • Keywords

Numerical radius, operator matrix, extension Buzano inequality, Young inequality.

  • AMS Subject Headings

47A12, 47A63

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JMS-58-323, author = {Gao , MuqileWu , Deyu and Chen , Alatancang}, title = {Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application}, journal = {Journal of Mathematical Study}, year = {2025}, volume = {58}, number = {3}, pages = {323--337}, abstract = {

We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds. Moreover, the conclusion is applied to the non-monic operator polynomials and gives a new bound for the eigenvalues of these operator polynomials.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v58n3.25.05}, url = {http://global-sci.org/intro/article_detail/jms/24411.html} }
TY - JOUR T1 - Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application AU - Gao , Muqile AU - Wu , Deyu AU - Chen , Alatancang JO - Journal of Mathematical Study VL - 3 SP - 323 EP - 337 PY - 2025 DA - 2025/09 SN - 58 DO - http://doi.org/10.4208/jms.v58n3.25.05 UR - https://global-sci.org/intro/article_detail/jms/24411.html KW - Numerical radius, operator matrix, extension Buzano inequality, Young inequality. AB -

We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds. Moreover, the conclusion is applied to the non-monic operator polynomials and gives a new bound for the eigenvalues of these operator polynomials.

Gao , MuqileWu , Deyu and Chen , Alatancang. (2025). Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application. Journal of Mathematical Study. 58 (3). 323-337. doi:10.4208/jms.v58n3.25.05
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