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Yet another method for bounding Jensen's functional for the operators on a Hilbert space (CROSBI ID 630297)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip Yet another method for bounding Jensen's functional for the operators on a Hilbert space. 2015

Podaci o odgovornosti

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip

engleski

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

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.

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

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Podaci o prilogu

2015.

objavljeno

Podaci o matičnoj publikaciji

Podaci o skupu

Mathematical inequalities and applications 2015

predavanje

11.11.2015-15.11.2015

Mostar, Bosna i Hercegovina

Povezanost rada

Matematika