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