Year: 2014
Type: article
Abstract: Using the same idea of the definition of means for pos- itive operators by Kubo and Ando, for each natural number $n$ , we can define means of two positive definite matrices of order $n$ and try to study the canonical map: we can describe an one to one corresponding from the class of matrix connections of order $n$ to the class of positive $n$ -monotone functions on $(0, \infty)$ and the range of this corresponding covers the class of interpolation functions of order $2n$ .In particular, the space of symmetric connections is iso- morphic to the space of symmetric positive $n$ -monotone functions.Moreover, we show that, for each $n$ , the class of $n$ -connections extremely contains that of $(n+2)$ -connections.
Authors: Trung Hoa Dinh, Ho Minh Toan, Hiroyuki Osaka
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1541689623