Induced norms, states, and numerical ranges
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- by Chi-Kwong Li, Edward Poon and Hans Schneider PDF
- Proc. Amer. Math. Soc. 132 (2004), 1501-1506 Request permission
Abstract:
It is shown that two induced norms are the same if and only if the corresponding norm numerical ranges or radii are the same, which in turn is equivalent to the vector states and mixed states arising from the norms being the same. The proofs depend on an auxiliary result of independent interest which concerns when two closed convex sets in a topological vector space are multiples of each other.References
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Additional Information
- Chi-Kwong Li
- Affiliation: Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795
- MR Author ID: 214513
- Email: ckli@math.wm.edu
- Edward Poon
- Affiliation: Department of Mathematics, Embry-Riddle Aeronautical University, 3200 Willow Creek Road, Prescott, Arizona 86301
- Email: edward.poon@erau.edu
- Hans Schneider
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- Email: hans@math.wisc.edu
- Received by editor(s): December 9, 2002
- Received by editor(s) in revised form: January 22, 2003
- Published electronically: September 18, 2003
- Additional Notes: Research partially supported by an NSF grant
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1501-1506
- MSC (2000): Primary 47A12, 47A30, 15A60
- DOI: https://doi.org/10.1090/S0002-9939-03-07213-7
- MathSciNet review: 2053358