## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 9, Number 3 (2015), 140-152.

### Interpolation classes and matrix means

Toan M. Ho, Dinh Trung Hoa, and Hiroyuki Osaka

#### Abstract

Using a `local' integral representation of a matrix connection of order $n$ corresponding to an interpolation function of the same order, for each integer $n$, we can describe an injective map 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 isomorphic 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.

#### Article information

**Source**

Banach J. Math. Anal., Volume 9, Number 3 (2015), 140-152.

**Dates**

First available in Project Euclid: 19 December 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1419001708

**Digital Object Identifier**

doi:10.15352/bjma/09-3-10

**Mathematical Reviews number (MathSciNet)**

MR3296130

**Zentralblatt MATH identifier**

1316.15037

**Subjects**

Primary: 46L30: States

Secondary: 15A45: Miscellaneous inequalities involving matrices

**Keywords**

Interpolation functions matrix monotone functions mean of positive matrices

#### Citation

Hoa, Dinh Trung; Ho, Toan M.; Osaka, Hiroyuki. Interpolation classes and matrix means. Banach J. Math. Anal. 9 (2015), no. 3, 140--152. doi:10.15352/bjma/09-3-10. https://projecteuclid.org/euclid.bjma/1419001708