Hölder Type Inequalities Involving Tracy-Singh Products and Khatri-Rao Products of Hilbert Space Operators

Authors

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

DOI:

https://doi.org/10.26713/cma.v10i3.1227

Keywords:

Hölder inequality, Tracy-Singh product, Khatri-Rao product, Hilbert space operator

Abstract

This paper generalizes the famous Hölder type inequalities for positive real numbers to positive operators on an arbitrary complex Hilbert space. We use appropriate integral representations of certain operator-monotone functions to deduce the concavity and convexity of certain maps involving Tracy-Singh products of operators. These results lead to Hölder type inequalities for operators concerning Tracy-Singh products, Khatri-Rao products, Tracy-Singh sums, and Khatri-Rao sums. In particular, we obtain Cauchy-Schwarz type inequalities for operators involving Tracy-Singh products and Khatri-Rao products.

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References

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Published

30-09-2019
CITATION

How to Cite

Ploymukda, A., & Chansangiam, P. (2019). Hölder Type Inequalities Involving Tracy-Singh Products and Khatri-Rao Products of Hilbert Space Operators. Communications in Mathematics and Applications, 10(3), 531–540. https://doi.org/10.26713/cma.v10i3.1227

Issue

Vol. 10 No. 3 (2019)

Section

Research Article

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