A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators

A. M. Nyongesa

doi:10.64388/IREV9I12-1718880

Home / Current Issue / Paper 1718880

1718880 Vol 9 · Issue 12 Download Paper

A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators

A. M. Nyongesa

Subject area: Science,Engineering and Technology · Area of research: Mathematics

DOI: 10.64388/IREV9I12-1718880

Abstract

We establish several multivariate refinements of Young’s inequality and extend them to τ-measurable operators affiliated with finite von Neumann algebras. Applications are obtained for determinants, spectral radius, Hilbert space operator means and noncommutative L_pnorms. In addition, we develop log-convex refinements and operator inequalities that strengthen previously known Young-type inequalities.

Keywords

Young Inequality, Operator Means, τ-Measurable Operators, Spectral Radius

References

[1] Igiachane, I., & Akkouchi, M. (2025). Further generalized refinement of Young inequalities. Moroccan Journal of Pure and Applied Analysis, to appear.

[2] Furuichi, S. (2011). Refined Young inequalities. Journal of Mathematical Analysis and Applications, 376, 467–476.

[3] Kittaneh, F. (2000). Matrix Young inequalities. Linear Algebra and Its Applications, 308, 217–224.

[4] Fuglede, B., & Kadison, R. (1952). Determinant theory in finite factors. Annals of Mathematics, 55, 520–530.

[5] Shao, J. (2017). Refined Young inequalities for τ-measurable operators. Linear and Multilinear Algebra, 65, 1070–1082.

[6] Ando, T. (1979). Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra and Its Applications, 26, 203–241.

[7] Bhatia, R., & Davis, C. (1993). More matrix forms of the arithmetic-geometric mean inequality. SIAM Journal on Matrix Analysis and Applications, 14, 132–136.

[8] Heinz, E. (1951). Beiträge zur Störungstheorie der Spektralzerlegung. Mathematische Annalen, 123, 415–438.

How to cite this paper

A. M. Nyongesa "A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators" Iconic Research And Engineering Journals Volume 9 Issue 12 2026 Page 1441-1445 https://doi.org/10.64388/IREV9I12-1718880

A. M. Nyongesa "A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators" Iconic Research And Engineering Journals, vol. 9, no. 12, Jun. 2026, doi: https://doi.org/10.64388/IREV9I12-1718880

A. M. Nyongesa (2026). A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators. Iconic Research And Engineering Journals, 9(12). doi: https://doi.org/10.64388/IREV9I12-1718880

A. M. Nyongesa "A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators" Iconic Research And Engineering Journals, vol. 9, no. 12, Jun. 2026. Crossref, https://doi.org/10.64388/IREV9I12-1718880

@article{1718880,
      author = {A. M. Nyongesa},
      title = {A Further Generalization of Young’s Inequalities for Multiple Variables and τ -measurable Operators},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {9},
      number = {12},
      pages = {1441-1445},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1718880.pdf},
      abstract = {We establish several multivariate refinements of Young’s inequality and extend them to τ-measurable operators affiliated with finite von Neumann algebras. Applications are obtained for determinants, spectral radius, Hilbert space operator means and noncommutative L_pnorms. In addition, we develop log-convex refinements and operator inequalities that strengthen previously known Young-type inequalities.},
      keywords = {Young Inequality, Operator Means, τ-Measurable Operators, Spectral Radius},
      month = {June},
      doi = {https://doi.org/10.64388/IREV9I12-1718880}
  }