Geometric Means and Tracy-Singh Products for Positive Operators

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.v9i4.547

Keywords:

Metric (spectral) geometric mean, Sagae-Tanabe metric (spectral) geometric mean, Tensor product, Tracy-Singh product, Khatri-Rao product

Abstract

We investigate relationship between metric/spectral/Sagae-Tanabe geometric means for several positive operators and Tracy-Singh products in terms of identities and inequalities. In particular, we obtain various generalizations of arithmetic-geometric-harmonic means inequality and its reverse. Moreover, we introduce the weighted Sagae-Tanabe spectral geometric mean for several positive operators and deduce its properties related to Tracy-Singh products.

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References

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Published

26-09-2018
CITATION

How to Cite

Ploymukda, A., & Chansangiam, P. (2018). Geometric Means and Tracy-Singh Products for Positive Operators. Communications in Mathematics and Applications, 9(4), 475–488. https://doi.org/10.26713/cma.v9i4.547

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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