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Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices

  • Kais Feki ORCID logo EMAIL logo and Satyajit Sahoo
Published/Copyright: November 24, 2022
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 30 Issue 2

Abstract

Let 𝔸 = ( A O O A ) be a 2 × 2 diagonal operator matrix whose each diagonal entry is a bounded positive (semi-definite) linear operator A acting on a complex Hilbert space ℋ . In this paper, we derive several 𝔸 -numerical radius inequalities for 2 × 2 operator matrices whose entries are bounded with respect to the seminorm induced by the positive operator A on ℋ . Some applications of our inequalities are also given.

Keywords: Positive operator; numerical radius; operator matrix; inequality
MSC 2010: 47A12; 46C05; 47B65; 47A05

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Received: 2022-04-15
Revised: 2022-07-22
Accepted: 2022-07-27
Published Online: 2022-11-24
Published in Print: 2023-04-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. B-essential spectra of 2 Ă— 2 block operator matrix pencils
  3. New results on perturbations of p-adic linear operators
  4. Approximation by matrix transform means with respect to the character system of the group of 2-adic integers
  5. Pentactions and action representability in the category of reduced groups with action
  6. On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
  7. Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices
  8. A generalization of practical stability of nonlinear impulsive systems
  9. Properties of rational Fourier series and generalized Wiener class
  10. Some identities on degenerate hyperharmonic numbers
  11. Generalized Pohozhaev’s identity for radial solutions of p-Laplace equations
  12. Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition
  13. Anisotropic nonlinear weighted elliptic equations with variable exponents
  14. Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has p;'-order
  15. Finite-time attractivity of strong solutions for generalized nonlinear abstract Rayleigh–Stokes equations
  16. Reproducing kernels and minimal solutions of elliptic equations
https://doi.org/10.1515/gmj-2022-2204
Keywords for this article
Positive operator; numerical radius; operator matrix; inequality

Articles in the same Issue

  1. Frontmatter
  2. B-essential spectra of 2 Ă— 2 block operator matrix pencils
  3. New results on perturbations of p-adic linear operators
  4. Approximation by matrix transform means with respect to the character system of the group of 2-adic integers
  5. Pentactions and action representability in the category of reduced groups with action
  6. On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded
  7. Further inequalities for the 𝔸-numerical radius of certain 2 × 2 operator matrices
  8. A generalization of practical stability of nonlinear impulsive systems
  9. Properties of rational Fourier series and generalized Wiener class
  10. Some identities on degenerate hyperharmonic numbers
  11. Generalized Pohozhaev’s identity for radial solutions of p-Laplace equations
  12. Classes of trivial ring extensions and amalgamations subject to pseudo-almost valuation condition
  13. Anisotropic nonlinear weighted elliptic equations with variable exponents
  14. Finite groups in which every non-nilpotent subgroup is a TI-subgroup or has p;'-order
  15. Finite-time attractivity of strong solutions for generalized nonlinear abstract Rayleigh–Stokes equations
  16. Reproducing kernels and minimal solutions of elliptic equations
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