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Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space (CROSBI ID 176711)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip Jensen's Operator and Applications to Mean Inequalities for Operators in Hilbert Space // Bulletin of the Malaysian Mathematical Sciences Society, 35 (2012), 1; 1-14

Podaci o odgovornosti

Krnić, Mario ; Lovričević, Neda ; Pečarić, Josip

engleski

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

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.

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

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Podaci o izdanju

35 (1)

2012.

1-14

objavljeno

0126-6705

Povezanost rada

Matematika

Indeksiranost