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Research articles

ScienceAsia 45 (2019): 194-201 |doi: 10.2306/scienceasia1513-1874.2019.45.194

Concavity and convexity of several maps involving Tracy-Singh products, Khatri-Rao products, and operator-monotone functions of positive operators

Arnon Ploymukda, Pattrawut Chansangiam*

ABSTRACT:     We establish concavity and convexity theorems for a number of operator-valued maps involving TracySingh products and Khatri-Rao products of positive operators on a Hilbert space. Operator means serve as useful tools for some convexity results. We also investigate certain maps dealing with positive operator-monotone functions. In this case, the concavity and the convexity of such maps are examined through suitable integral representations of the operator-monotone functions on the unit interval with respect to finite Borel measures.

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a Department of Mathematics, Faculty of Science, King Mongkut?s Institute of Technology Ladkrabang, Bangkok 10520 Thailand

* Corresponding author, E-mail: pattrawut.ch@kmitl.ac.th

Received 12 Nov 2018, Accepted 27 Mar 2019