Geodesic
Numerical Range and Convex Sets*
Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 295-296

Voir la notice de l'article provenant de la source Cambridge University Press

The numerical range W(T) of a bounded linear operator T on a Hilbert space H is defined by W(T) is always a convex subset of the plane [1] and clearly W(T) is bounded since it is contained in the ball of radius ‖T‖ about the origin. Which non-empty convex bounded subsets of the plane are the numerical range of an operator? The theorem we prove below shows that every non-empty convex bounded subset of the plane is W(T) for some T.
DOI : 10.4153/CMB-1974-058-3
Mots-clés : 4710, 5230 
Numerical Range and Convex Sets*. Canadian mathematical bulletin, Tome 17 (1974) no. 2, pp. 295-296. doi: 10.4153/CMB-1974-058-3
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[1] 1. Halmos, P. R., A Hilbert space problem book, Van Nostrand, Princeton, 1967. Google Scholar

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