Jensen’s Type Inequalities Involving Tracy-Singh Products, Khatri-Rao Products, Tracy-Singh Sums and Khatri-Rao Sums

Arnon Ploymukda, Pattrawut Chansangiam

Abstract

In this paper, we establish a number of Jensen’s type inequalities for Hilbert space operators involving convex/concave functions, unital positive linear maps, and certain operator products and sums. The products and sums considered here include the Tracy-Singh product, the Khatri-Rao products, the Tracy-Singh sum, and the Khatri-Rao sum. Moreover, we generalize Jensen’s type inequalities in term of functional calculus of two-variable functions. In particular, we obtain Kantorovich-type operator inequalities involving the products and sums.