Naslov
Yet another method for bounding Jensen's functional for the operators on a Hilbert space

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

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Skup
Mathematical Inequalities and Applications 2015

Mjesto i datum
Mostar, Bosna i Hercegovina, 11.11.2015. - 15.11.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Jensen's inequality; Jensen's functional; Hilbert space; bounded self-adjoint operator; positive invertible operator; arithmetic operator mean; geometric operator mean; harmonic operator mean; refinement; converse; Kantorovich constant

Sažetak
Jensen's functional for the operators on a Hilbert space is deduced from the discrete Jensen's functional. Real arguments of such functional are substituted by the bounded self-adjoint operators on a Hilbert space. Under the assumption of convexity of the included function, both functionals are proved to be superadditive and increasing on the set of all weight n-tuples described in definition, which provides us with the specific bounds of the considered functionals and, in the case of the functional for the operators, with the method for refinements and converses of the existing inequalities for certain operator means (arithmetic, geometric, harmonic and Heinz means). Except for this method, yet another one is employed in a similar sense which provides us with another type of such bounds and, consequently, with refinements and converses of the mentioned inequalities. This method regards a specific monotonicity property of Jensen's functional considered as a function of one variable and interprets its bounds as the estimates for the spectrum of Jensen's functional for the operators on a Hilbert space.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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