Naslov
Multidimensional Jensen's operator on a Hilbert space and applications

Autori
Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip

Izvornik
Linear algebra and its applications (0024-3795) 436 (2012), 7; 2583-2596

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jensen's operator inequality; operator convexity; operator concavity; multidimensional Jensen's operator; Jensen's integral operator; connection; solidarity; the relative operator entropy; multidimensional weighted geometric mean

Sažetak
Motivated by a joint concavity of connections, solidarities and multidimensional weighted geometric mean, in this paper we extend an idea of convexity (concavity) to operator functions of several variables. With the help of established definitions, we introduce the so called multidimensional Jensen's operator and study its properties. In such a way we get the lower and upper bounds for the above mentioned operator, expressed in the terms of the non-weighted operator of the same type. As an application, we obtain both refinements and converses for operator variants of some well known classical inequalities. In order to obtain the refinements of Jensen's integral inequality, we also consider an integral analogue of Jensen's operator for functions of one variable.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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