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Proceedings of the American Mathematical Society Series B

ISSN 2330-1511

   
 
 

 

Unexpected relations which characterize operator means


Authors: Hiroyuki Osaka and Shuhei Wada
Journal: Proc. Amer. Math. Soc. Ser. B 3 (2016), 9-17
MSC (2010): Primary 47A64, 47A63
DOI: https://doi.org/10.1090/bproc/23
Published electronically: November 30, 2016
MathSciNet review: 3577892
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Abstract: We give some characterizations of self-adjointness and symmetricity of operator monotone functions by using the Barbour transform $f \mapsto \frac {t+f}{1+f}$ and show that there are many non-symmetric operator means between the harmonic mean $!$ and the arithmetic mean $\nabla$. Indeed, we show that there exists a non-symmetric operator mean between any two symmetric operator means.


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Additional Information

Hiroyuki Osaka
Affiliation: Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga 525-8577, Japan
MR Author ID: 290405

Shuhei Wada
Affiliation: Department of Information and Computer Engineering, Kisarazu National College of Technology, Kisarazu, Chiba 292-0041, Japan
MR Author ID: 270829
Email: wada@j.kisarazu.ac.jp

Keywords: Barbour transformation, operator monotone functions, operator connections, symmetric operator means, self-adjoint operator means
Received by editor(s): February 20, 2016
Received by editor(s) in revised form: June 18, 2016
Published electronically: November 30, 2016
Additional Notes: The first author partially supported by the Program for Promotion of International Research (2014) (Ritsumeikan University)
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2016 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)