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Approximations of positive operators and continuity of the spectral radius III

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

F. Aràndiga  and
V. Caselles
F. Aràndiga
Affiliation:
Department de Matemàtica, Aplicada i Astronomia, Universitat de Valencia, Dr. Moliner, 50 46100-Burjassot (Valencia), Spain
V. Caselles
Affiliation:
Department de Matemàtiques, i Informàtica, Universitat de les Illes Balears, Ctra. Valldemossa, km. 7.5, 07071 Palma de Mallorca (Balears), Spain
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Abstract

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We prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.

MSC classification

Secondary: 47A10: Spectrum, resolvent

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 330 - 340
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Arandiga, F. and Caselles, V., ‘Approximations of positive operators and continuity of the spectral radius’, J. Operator Theory 26 (1991), 53–71.Google Scholar
[2]Arandiga, F. and Caselles, V., ‘Approximations of positive operators and continuity of the spectral radius II’, Math. Z. 209 (1992), 547–558.CrossRefGoogle Scholar
[3]Asadzadeh, M., ‘Lp and eigenvalue error estimates for discrete ordinates method for two-dimensional neutron transport’, SIAM J. Numer. Anal. 26 (1989), 66–87.Google Scholar
[4]Boyd, M. W. and Transue, W. R., ‘Properties of ultraproduct’, Rend. Circ. Mat. Palermo 28 (1979), 387–397.Google Scholar
[5]Caselles, V., ‘On irreducible operators on Banach lattices’, Indag. Math. 89 (1986), 11–16.Google Scholar
[6]Caselles, V., ‘On the peripheral spectrum of positive operators’, Israel J. Math. 58 (1986), 144–160.Google Scholar
[7]Chatelin, F., Spectral approximation of linear operators (Academic Press, New York, 1983).Google Scholar
[8]Dunford, N. and Schwartz, T., Linear operators I (Wiley, New York, 1958).Google Scholar
[9]Marek, I., ‘Approximations of the principal eigenelements in K-positive nonselfadjoint eigenvalue problems’, Math. Systems Theory 5 (1971), 204–215.Google Scholar
[10]Moustakas, U., Majorisierung und Spektraleigenschaften positiver Operatoren auf Banachverbaenden (Dissertation, University of Tuebinger, 1984).Google Scholar
[11]Schaefer, H. H., Banach lattices and positive operators (Springer, Berlin, 1974).CrossRefGoogle Scholar
[12]Zaanen, A. C., Riesz spaces II (North-Holland, Amsterdam, 1983).Google Scholar