Naslov
Inequalities between operator means based on the Mond-Pečarić method and its applications

Autori
Mićić, Jadranka ; Pečarić, Josip ; Seo, Yuki

Izvornik
Bulletin of the Institute for Chemical Research, Kyoto University (0023-6071) 2 (2001); 1-9

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

Ključne riječi
operator means; Mond-Pečaric method; operator entropy; operator divergence

Sažetak
In this paper, we shall consider the estimates of $\alpha$-operator divergence by terms of the spectra of positive operators. For this purpose, we shall investigate the estimates of the difference of two operator means in general setting. We prove that for positive invertible operators $A$, $B$ and a given $\alpha >0$, there exists the most suitable real number $\beta $ such that $$\Phi (A \sigma_1 B)\geq \alpha \Phi (A) \sigma _2 \Phi (B) +\beta \Phi (A)$$ where $\Phi $ is a unital positive linear map and $\sigma _1$, $\sigma _2$ are operator means. In particular, if we put $\alpha =1$ and $\Phi $ is the identity map, then we have the lower bound of the difference of $A\ \sigma _1 \ B$ and $A\ \sigma _2 \ B$. Consequently we obtain the estimates of $\alpha$-operator divergence by terms of the spectra of positive operators.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Elektrotehnika

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