Naslov
Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space

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

Izvornik
Bulletin of the Malaysian Mathematical Sciences Society (0126-6705) 35 (2012), 1; 1-14

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

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

Sažetak
In this paper we consider Jensen's operator, which includes bounded self-adjoint operator on Hilbert space, and investigate its properties. Due to the derived properties, we find lower and upper bound for Jensen's operator, which are multiples of non-weighted Jensen's operator. On the other hand, we also establish some bounds for spectra of Jensen's operator by means of discrete Jensen's functional. The obtained results are then applied to operator means. In such way we get refinements and conversions of numerous mean inequalities for Hilbert space operators.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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