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Analytic functions of a prespectral operator

Published online by Cambridge University Press:  18 May 2009

S. Al-Khezi
S. Al-Khezi
Affiliation:
Department of Mathematics, University of Glasgow.
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The purpose of this note is to present a unified treatment of the material contained in Chapter 10 of [2] on roots and logarithms of prespectral operators. Our main result gives a sufficient condition for an analytic function of a prespectral operator of class Γ to be prespectral of class Γ. A result in the opposite direction for spectral operators has been obtained by Apostol [1]. Terminology and notation in this paper are as in [2].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 171 - 175
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Apostol, C., On the roots of spectral operator-valued analytic functions, Rev. Roumaine Math. Pures Appl. 13 (1968), 587–589.Google Scholar
2.Dowson, H. R., Spectral theory of linear operators (Academic Press, 1978).Google Scholar
3.Rudin, W., Real and complex analysis (McGraw Hill, 1966).Google Scholar