J Austral Math Soc Ser A 57 pp330--340, 1994.

Approximations of Positive Operators and Continuity of the Spectral Radius III

F. Arandiga and V. Caselles

Abstract

We prove estimates on the speed of the convergence of the 'peripheral eigenvalues' (and principal eigenvectors) of a sequence T_n 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 T_n to T. These results sharpen results of convergence obtained by the authors in previous papers.

1991 AMS Subject Classification: 47B55, 47A10, 46B30

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Authors

F. Arandiga

Department de Matematica, Aplicada i Astronomia, Universitat de Valencia, Dr. Moliner, 50, 46100-Burjassot (Valencia), Spain.

V. Caselles

Department de Matematiques, i Informatica, Universitat de les Illes Balears, Ctra. Valldemossa, km. 7.5, 07071 Palma de Mallorca (Balears), Spain.