Numerical range estimates for the norms of iterated operators
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 85-87

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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.
Crabb, M. J. Numerical range estimates for the norms of iterated operators. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 85-87. doi: 10.1017/S0017089500000896
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