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Numerical Range and Convex Sets*

Published online by Cambridge University Press:  20 November 2018

Fredric M. Pollack
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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.

Keywords

47105230
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 295 - 296
Copyright
Copyright © Canadian Mathematical Society 1974

Footnotes

*

Partially supported by NSF Grant #GP-6727.

References

1. Halmos, P. R., A Hilbert space problem book, Van Nostrand, Princeton, 1967.Google Scholar