Analytic functions of a prespectral operator
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 171-175
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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].
Al-Khezi, S. Analytic functions of a prespectral operator. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 171-175. doi: 10.1017/S0017089500004948
@article{10_1017_S0017089500004948,
author = {Al-Khezi, S.},
title = {Analytic functions of a prespectral operator},
journal = {Glasgow mathematical journal},
pages = {171--175},
year = {1982},
volume = {23},
number = {2},
doi = {10.1017/S0017089500004948},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004948/}
}
[1] 1.Apostol, C., On the roots of spectral operator-valued analytic functions, Rev. Roumaine Math. Pures Appl. 13 (1968), 587–589. Google Scholar
[2] 2.Dowson, H. R., Spectral theory of linear operators (Academic Press, 1978). Google Scholar
[3] 3.Rudin, W., Real and complex analysis (McGraw Hill, 1966). Google Scholar
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