F. Arandiga et V. Caselles, APPROXIMATIONS OF POSITIVE OPERATORS AND CONTINUITY OF THE SPECTRAL RADIUS-III, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 57, 1994, pp. 330-340
Citations number
12
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
We prove estimates on the speed of convergence of the 'peripheral eige
nvalues' (and principal eigen-vectors) of a sequence T(n) of positive
operators on a Banach lattice E to the peripheral eigenvalues of its l
imit 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 resu
lts sharpen results of convergence obtained by the authors in previous
papers.