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Numerical range estimates for the norms of iterated operators

Published online by Cambridge University Press:  18 May 2009

M. J. Crabb
M. J. Crabb
Affiliation:
University of Edinburgh
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Let X be a complex normed space, with dual space X′, and T a bounded linear operator on X. The numerical range V(T) of T is defined as {f(Tx): x∊X, f∊ X′, ∥x∥ = ∥f∥ = f(x) = 1}. Let ⃒V(T)⃒ denote sup {⃒λ⃒: λ∊ V(T)}. Our purpose is to prove the following theorem.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 2 , July 1970 , pp. 85 - 87
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

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