Banach Journal of Mathematical Analysis

Interpolation classes and matrix means

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 19 December 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L30: States
Secondary: 15A45: Miscellaneous inequalities involving matrices

Interpolation functions matrix monotone functions mean of positive matrices


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.

Export citation