Naslov
Order among power means of positive operators

Autori
Mićić, Jadranka ; Pečarić, Josip

Izvornik
Scientiae mathematicae Japonicae (1346-0862) 61 (2005), 1; 15-36

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

Ključne riječi
Operator order; Mond-Pe\v{;; c};; ari\'{;; c};; method; weighted

Sažetak
As a continuation of our paper [Sci. Math. Japon., {; ; \bf 57}; ; (2003), 139--148] we determined real constants $\alpha_1$, $\alpha_2$, $\beta_1$ and $\beta_2$ such that $$\alpha_2 M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; , {; ; \mathbf{; ; \Phi}; ; }; ; , {; ; \mathbf{; ; \omega}; ; }; ; ) \leq M_{; ; k}; ; ^{; ; [r]}; ; ({; ; \mathbf{; ; A}; ; }; ; , {; ; \mathbf{; ; \Phi}; ; }; ; , {; ; \mathbf{; ; \omega}; ; }; ; ) \leq \alpha_1 M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; , {; ; \mathbf{; ; \Phi}; ; }; ; , {; ; \mathbf{; ; \omega}; ; }; ; )$$ and $$ \beta_2 I \leq M_{; ; k}; ; ^{; ; [s]}; ; ({; ; \mathbf{; ; A}; ; }; ; , {; ; \mathbf{; ; \Phi}; ; }; ; , {; ; \mathbf{; ; \omega}; ; }; ; ) - M_{; ; k}; ; ^{; ; [r]}; ; ({; ; \mathbf{; ; A}; ; }; ; , {; ; \mathbf{; ; \Phi}; ; }; ; , \mathbf\omega}; ; }; ; ) \leq \beta_1 I$$ hold if $r \leq s$, $r, s \neq 0$. As applications, these inequalities for some special maps were given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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