SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions

Shaohua Pan Yungyen Chiang Jein-Shan Chen

Functional Analysis mathscidoc:1910.43927

Linear Algebra and its Applications, 437, (5), 1264-1284, 2012.9
The SOC-monotone function (respectively, SOC-convex function) is a scalar valued function that induces a map to preserve the monotone order (respectively, the convex order), when imposed on the spectral factorization of vectors associated with second-order cones (SOCs) in general Hilbert spaces. In this paper, we provide the sufficient and necessary characterizations for the two classes of functions, and particularly establish that the set of continuous SOC-monotone (respectively, SOC-convex) functions coincides with that of continuous matrix monotone (respectively, matrix convex) functions of order 2.
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@inproceedings{shaohua2012soc-monotone,
  title={SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions},
  author={Shaohua Pan, Yungyen Chiang, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225030879970456},
  booktitle={Linear Algebra and its Applications},
  volume={437},
  number={5},
  pages={1264-1284},
  year={2012},
}
Shaohua Pan, Yungyen Chiang, and Jein-Shan Chen. SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions. 2012. Vol. 437. In Linear Algebra and its Applications. pp.1264-1284. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225030879970456.
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