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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}.

Information

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

References

REFERENCES

1.de Barra, G., Some algebras of operators with closed convex numerical range, Proc. Roy. Irish Acad. 72 (1972), 149–154.Google Scholar
2.de Barra, G., Generalized limits and uniform convexity. Proc. Roy. Irish Acad. 74 (1974), 73–77.Google Scholar
3.Beauzamy, B., Introduction to Banach spaces and their geometry (North-Holland, 1985).Google Scholar
4.Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras (Cambridge, 1971).Google Scholar
5.Bonsall, F. F. and Duncan, J., Numerical ranges II (Cambridge, 1973).CrossRefGoogle Scholar
6.Chō, M., Joint spectra of operators on Banach space, Glasgow Math. J. 28 (1986), 69–72.CrossRefGoogle Scholar
7.Chō, M., Joint spectra of commuting normal operators on Banach spaces, Glasgow Math J. 30 (1988), 339–345.Google Scholar
8.Chō, M., Hyponormal operators on uniformly convex spaces, Acta Sci. Math. (Szeged), to appear.Google Scholar
9.Chō, M. and Dash, A. T., On the joint spectra of doubly commuting n-tuples of semi-normal operators, Glasgow Math. J. 26 (1985), 47–50.CrossRefGoogle Scholar
10.Chō, M. and Yamaguchi, H., Bare points of joint numerical ranges for doubly commuting hyponormal operators on strictly c-convex spaces, preprint.Google Scholar
11.Mattila, K., Normal operators and proper boundary points of the spectra of operators on Banach space, Ann. Acad. Sci. Fenn. AI Math. Dissertationes 19 (1978).Google Scholar
12.Mattila, K., Complex strict and uniform convexity and hyponormal operators, Math. Proc. Cambridge Philos. Soc. 96 (1984), 483–497.CrossRefGoogle Scholar
13.Putnam, C. R., Commutation properties of Hilbert space operators and related topics. (Springer, 1967).Google Scholar