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Numerical range estimates for the norms of iterated operators
Published online by Cambridge University Press: 18 May 2009
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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.
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- Copyright © Glasgow Mathematical Journal Trust 1970
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