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The numerical range of an element of a normed algebra

Published online by Cambridge University Press:  18 May 2009

F. F. Bonsall
F. F. Bonsall
Affiliation:
University of Edinburgh
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Given a normed linear space X, let S(X), X′, B(X) denote respectively the unit sphere {x: ∥x∥ = 1} of X, the dual space of X, and the algebra of all bounded linear mappings of X into X. For each x ∊ S(X) and T ∊ B(X), let Dx(x) = {f e X′:∥f∥ = f(x)= 1}, and V(T; x) = {f(Tx):f∊Dx(x)}. The numerical range V(T) is then defined by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 1 , January 1969 , pp. 68 - 72
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

REFERENCES

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