Naslov
Some functions reversing the order of positive operators

Autori
Pečarić, Josip ; Mićić, Jadranka

Izvornik
Linear algebra and its applications (0024-3795) 396 (2005); 175-187

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

Ključne riječi
operator order; generalized Kantorovich constant; Mond-Pečri\ćmethod; weighted power mean

Sažetak
As a complement to our previous results about the function preserving the operator order, we shall show the following reversing version: Let $A$ and $B$ be positive operators on a Hilbert space $H$ satisfying $MI\geq B\geq mI>0$. Let $f(t)$ be a continuous convex function on $[m, M]$. If $g(t)$ is a continuous decreasing convex function on $[m, M]\cup {;\mathsf{;Sp};};(A)$, then for a given $\alpha >0$ \begin{;equation*};A\geq B\geq 0 \quad \text{;implies};\quad \alpha g(B)+ \beta I \geq f(A) \end{;equation*}; where $\beta =\max _{;m\leq t\leq M};\{;f(m)+(f(M)-f(m))(t-m)/(M-m)-\alpha g(t) \};$. Our main result is to classify complementary inequalities on power means of positive operators.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA