Local characterizations for the matrix monotonicity and convexity of fixed order

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http://hdl.handle.net/10138/307505

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Heinavaara , O 2018 , ' Local characterizations for the matrix monotonicity and convexity of fixed order ' , Proceedings of the American Mathematical Society , vol. 146 , no. 9 , pp. 3791-3799 . https://doi.org/10.1090/proc/13674

Title: Local characterizations for the matrix monotonicity and convexity of fixed order
Author: Heinavaara, Otte
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2018-07-15
Language: eng
Number of pages: 9
Belongs to series: Proceedings of the American Mathematical Society
ISSN: 0002-9939
URI: http://hdl.handle.net/10138/307505
Abstract: We establish local characterizations of matrix monotonicity and convexity of fixed order by giving integral representations connecting the Loewner and Kraus matrices, previously known to characterize these properties, to respective Hankel matrices. Our results are new already in the general case of matrix convexity, and our approach significantly simplifies the corresponding work on matrix monotonicity. We also obtain an extension of the original characterization for matrix convexity by Kraus and tighten the relationship between monotonicity and convexity.
Subject: Matrix monotone functions
matrix convex functions
111 Mathematics
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