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Semi-normal operators on uniformly smooth Banach spaces
Published online by Cambridge University Press: 18 May 2009
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In this paper we shall examine the relationship between the numerical ranges and the spectra for semi-normal operators on uniformly smooth spaces.
Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. A linear functional F on B(X) is called state if ∥F∥ = F(I) = 1. When x ε X with ∥x∥ = 1, we denote
D(x) = {f ε X*:∥f∥ = f(x) = l}.
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- Copyright © Glasgow Mathematical Journal Trust 1990
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