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

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• 作者：Shaohua Pan ; Yungyen Chiang ; Jein-Shan Chen
• 关键词：26B05 ; 26B35 ; 90C33 ; 65K05
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 出版时间：1 September, 2012
• 年：2012
• 卷：437
• 期：5
• 页码：1264-1284
• 全文大小：405 K

文摘

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.