Refinements and Reverses of Operator Callebaut Inequality Involving Tracy-Singh Products and Khatri-Rao Products

Authors

  • Arnon Ploymukda Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520
  • Pattrawut Chansangiam Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520

DOI:

https://doi.org/10.26713/cma.v9i4.1096

Keywords:

Callebaut inequality, Tracy-Singh product, Khatri-Rao product, Weighted geometric mean, Continuous field of operators

Abstract

In this paper, we establish certain refinements and reverses of Callebaut-type inequality for bounded continuous fields of Hilbert space operators, parametrized by a locally compact Hausdorff space equipped with a finite Radon measure. These inequalities involve Tracy-Singh products, Khatri-Rao products and weighted geometric means. In addition, we obtain integral Callebauttype inequalities for tensor products and Hadamard products. Our results extend Callebaut-type inequalities for real numbers, matrices and operators.

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References

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Published

25-12-2018
CITATION

How to Cite

Ploymukda, A., & Chansangiam, P. (2018). Refinements and Reverses of Operator Callebaut Inequality Involving Tracy-Singh Products and Khatri-Rao Products. Communications in Mathematics and Applications, 9(4), 529–540. https://doi.org/10.26713/cma.v9i4.1096

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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