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Multidimensional Jensen's operator on a Hilbert space and applications (CROSBI ID 176716)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip Multidimensional Jensen's operator on a Hilbert space and applications // Linear algebra and its applications, 436 (2012), 7; 2583-2596. doi: 10.1016/j.laa.2011.09.013

Podaci o odgovornosti

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip

engleski

Multidimensional Jensen's operator on a Hilbert space and applications

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.

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

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Podaci o izdanju

436 (7)

2012.

2583-2596

objavljeno

0024-3795

10.1016/j.laa.2011.09.013

Povezanost rada

Matematika

Poveznice
Indeksiranost