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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Numerical range, dilation, and completely positive maps
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by Chi-Kwong Li and Yiu-Tung Poon PDF
Proc. Amer. Math. Soc. 147 (2019), 4805-4811 Request permission

Abstract:

A proof using the theory of completely positive maps is given to the fact that if $A \in M_2$ or $A \in M_3$ has a reducing eigenvalue, then every bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the form $I \otimes A$. This gives a unified treatment for the different cases of the result obtained by researchers using different techniques.
References
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Additional Information
  • Chi-Kwong Li
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsbug, Virginia 23187
  • MR Author ID: 214513
  • Email: ckli@math.wm.edu
  • Yiu-Tung Poon
  • Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
  • MR Author ID: 141040
  • Email: ytpoon@iastate.edu
  • Received by editor(s): January 18, 2019
  • Received by editor(s) in revised form: February 3, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: The research of the first author was supported by USA NSF grant DMS 1331021, Simons Foundation grant 351047, and NNSF of China grant 11571220.
  • Communicated by: Stephan Ramon Garcia
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4805-4811
  • MSC (2010): Primary 47A12, 47A30, 15A60
  • DOI: https://doi.org/10.1090/proc/14582
  • MathSciNet review: 4011514