Local characterizations for the matrix monotonicity and convexity of fixed order
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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.References
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Additional Information
- Otte Heinävaara
- Affiliation: Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hällströmin katu 2b), FI-00014 University of Helsinki, Finland
- Email: otte.heinavaara@helsinki.fi
- Received by editor(s): September 15, 2016
- Received by editor(s) in revised form: January 26, 2017
- Published electronically: May 24, 2018
- Communicated by: Stephan Ramon Garcia
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3791-3799
- MSC (2010): Primary 26A48; Secondary 26A51, 47A63
- DOI: https://doi.org/10.1090/proc/13674
- MathSciNet review: 3825834