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Induced norms, states, and numerical ranges |
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| Authors: | Chi-Kwong Li Edward Poon Hans Schneider |
| Institution: | Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795 ; Department of Mathematics, Embry-Riddle Aeronautical University, 3200 Willow Creek Road, Prescott, Arizona 86301 ; Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706 |
| 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. |
| Keywords: | Induced norms vector states mixed states norm numerical ranges |
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