On numerical diameters and linear maps
Faculty Advisor
Date
2024
Keywords
Hilbert space, induced seminorm, numerical diameter
Abstract (summary)
This paper studies the diameter of the numerical range of bounded operators on Hilbert space and the induced seminorm, called the numerical diameter, on bounded linear maps between operator systems which is sensible in the case of unital maps and their scalar multiples. It is shown that the completely bounded numerical diameter is a norm that is comparable but not equal to the completely bounded norm. This norm is particularly interesting in the case of unital completely positive maps and their sections.
Publication Information
de Beaudrap, N., & Ramsey, C. (2024). On numerical diameters and linear maps. New York Journal of Mathematics, 30, 1264-1292. https://nyjm.albany.edu/j/2024/30-56.html
DOI
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Item Type
Article
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Attribution (CC BY)
