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
Full-text PDF Open Access
View in AMS MathViewer
Abstract | References | Similar Articles | Additional Information
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)
