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

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

Izvornik
Houston journal of mathematics (0362-1588) 30 (2004), 1; 191-207

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

Ključne riječi
operator inequality; positive linear map; mixed means

Sažetak
As a continuation of our previous paper (Complementary inequalities to inequalities of Jensen and Ando based on Mond- Pecaric method, Linear Alg. Appl., 318 (2000), 87-107) we show further general complementary inequalities to operator inequalities on a positive linear map associated with two operator means. Let $A$ and $B$ be positive invertible operators on a Hilbert space $H$, $\sigma, \tau$ two operator means and $\Phi $ a positive linear map. If $\alpha >0$ is a given real constant, then real constants $\beta $ and $\beta ^0$ such that \begin{; ; align*}; ; \Phi (A \ \sigma \ B) & \geq \alpha \Phi (A) \ \tau \ \Phi (B) +\beta \Phi (A), \\ \Phi (A \ \sigma \ B) & \geq \alpha \Phi (A) \ \tau \ \Phi (B) +\beta ^0 \Phi (B) \end{; ; align*}; ; are determined. As applications, we obtain general complementary estimates for the results by Aujla-Vasudeva \cite{; ; AV2}; ; and J.I.Fujii \cite{; ; JIF}; ; on the Hadamard product and operator means, and Mond-Pe\v{; ; c}; ; ari\'{; ; c}; ; -\v{; ; S}; ; unde-Varo\v{; ; s}; ; anec \cite{; ; MPSV}; ; on several mixed operator means.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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