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arXiv · 1105.3881

Higher order extension of L\"owner's theory: Operator $k$-tone functions

Uwe Franz·Fumio Hiai·Éric Ricard
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Abstract

The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations, properties, and examples of operator $k$-tone functions are presented. In particular, integral representations of operator $k$-tone functions are given, generalizing familiar representations of operator monotone and convex functions.

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Uwe Franz, Fumio Hiai, Éric Ricard. 2011-05-19. Higher order extension of L\"owner's theory: Operator $k$-tone functions. https://doi.org/10.1090/s0002-9947-2014-05942-4

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