Higher order extension of Löwner's theory: Operator $k$-tone functions

Details Higher order extension of Löwner's theory: Operator $k$-tone functions Higher order extension of Löwner's theory: Operator $k$-tone functions

2011-05-19

arxiv.org/abs/1105.3881v3

Mathematics

Functional Analysis

44 pages

Scientific paper

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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