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