On the ideal structure of positive, eventually compact linear operators on banach lattices

Ruey Jen Jang-Lewis, J. Harold Dean Victory

Research output: Contribution to journalArticle

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Abstract

We study the structure of the algebraic eigenspace corresponding to the spectral radius of a nonnegative reducible linear operator T, having a compact iterate and defined on a Banach lattice E with order continuous norm. The Perron-Frobenius theory is generalized by showing that this algebraic eigenspace is spanned by a basis of eigenelements and generalized eigenelements possessing certain positivity features. A combinatorial characterization of both the Riesz index of the spectral radius and the dimension of the algebraic eigenspace is given. These results are made possible by a decomposition of T, in terms of certain closed ideals of E, in a form which directly generalizes the Frobenius normal form of a nonnegative reducible matrix.

Original languageEnglish
Pages (from-to)57-85
Number of pages29
JournalPacific Journal of Mathematics
Volume157
Issue number1
DOIs
StatePublished - Jan 1993

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