Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Numerical range, dilation, and completely positive maps


Authors: Chi-Kwong Li and Yiu-Tung Poon
Journal: Proc. Amer. Math. Soc. 147 (2019), 4805-4811
MSC (2010): Primary 47A12, 47A30, 15A60
DOI: https://doi.org/10.1090/proc/14582
Published electronically: June 10, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47A12, 47A30, 15A60

Retrieve articles in all journals with MSC (2010): 47A12, 47A30, 15A60


Additional Information

Chi-Kwong Li
Affiliation: Department of Mathematics, College of William and Mary, Williamsbug, Virginia 23187
Email: ckli@math.wm.edu

Yiu-Tung Poon
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: ytpoon@iastate.edu

DOI: https://doi.org/10.1090/proc/14582
Keywords: Numerical range, dilation, operator system, positive and completely positive map.
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
Article copyright: © Copyright 2019 American Mathematical Society