Geometric eigenspace of the generator of C0-semigroup of positive operators

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Abstract

Let E be a Banach lattice with order continuous norm and {T(t)}t≥0 be an eventually compact c0-semigroup of positive operators on E with generator A. We investigate the structure of the geometric eigenspace of the generator belonging to the spectral bound when the semigroup is ideal reducible. It is shown that a basis of the eigenspace can be chosen to consist of elements of E with certain positivity structure. This is achieved by a decomposition of the underlying Banach lattice E into a direct sum of closed ideals which can be viewed as a generalization of the Frobenius normal form for nonnegative reducible matrices.

Original languageEnglish
Pages (from-to)292-304
Number of pages13
JournalIntegral Equations and Operator Theory
Volume39
Issue number3
DOIs
StatePublished - Mar 2001

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