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Semi-normal operators on uniformly smooth Banach spaces

Published online by Cambridge University Press:  18 May 2009

Muneo Chō
Muneo Chō
Affiliation:
Department of MathematicsJoetsu University of EducationJoetsu, Niigata 943Japan
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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}.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 273 - 276
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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