Title : ( A normal family of operator monotone functions )
Authors: Mohammad Sal Moslehian , Hamed Najafi , Mitsuru Uchiyama ,
دانلود فایل برای اعضای دانشگاهAccess to full-text not allowed by authors
Abstract
We show that the family of all operator monotone functions $f$ on $(-1,1)$ such that $f(0)=0$ and $f^{\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\'}(0)=1$ is a normal family and investigate some properties of odd operator monotone functions. We also characterize the odd operator monotone functions and even operator convex functions on $(-1,1)$. As a consequence, we show that if $f$ is an odd operator monotone function on $(-1,1)$, then $f$ is concave on $(-1,0)$ and convex on $(0,1)$.
Keywords
Operator monotone function; operator convex function; normal family; integral representation
@article{paperid:1026766,
author = {Sal Moslehian, Mohammad and Najafi, Hamed and Mitsuru Uchiyama},
title = {A normal family of operator monotone functions},
journal = {Hokkaido Mathematical Journal},
year = {2013},
volume = {42},
number = {3},
month = {November},
issn = {0385-4035},
pages = {417--423},
numpages = {6},
keywords = {Operator monotone function; operator convex function;
normal family; integral representation},
}
%0 Journal Article
%T A normal family of operator monotone functions
%A Sal Moslehian, Mohammad
%A Najafi, Hamed
%A Mitsuru Uchiyama
%J Hokkaido Mathematical Journal
%@ 0385-4035
%D 2013
