SOC-monotone and SOC-convex functions vs. matrix-monotone and matrix-convex functions |
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Authors: | Shaohua Pan Yungyen Chiang Jein-Shan Chen |
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Institution: | 1. Department of Mathematics, South China University of Technology, Wushan Road 381, Tianhe District, Guangzhou 510641, China;2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan;3. Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan |
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Abstract: | 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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