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2015 Interpolation classes and matrix means
Toan M. Ho, Dinh Trung Hoa, Hiroyuki Osaka
Banach J. Math. Anal. 9(3): 140-152 (2015). DOI: 10.15352/bjma/09-3-10

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.

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Toan M. Ho. Dinh Trung Hoa. Hiroyuki Osaka. "Interpolation classes and matrix means." Banach J. Math. Anal. 9 (3) 140 - 152, 2015. https://doi.org/10.15352/bjma/09-3-10

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1316.15037
MathSciNet: MR3296130
Digital Object Identifier: 10.15352/bjma/09-3-10

Subjects:
Primary: 46L30
Secondary: 15A45

Keywords: interpolation functions , matrix monotone functions , mean of positive matrices

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 3 • 2015
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