Numerical range estimates for the norms of iterated operators

1 July 1970

journal article
research article
Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal

Vol. 11 (2) , 85-87
https://doi.org/10.1017/s0017089500000896

Abstract

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.

Keywords

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