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 language | English |
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Pages (from-to) | 292-304 |
Number of pages | 13 |
Journal | Integral Equations and Operator Theory |
Volume | 39 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2001 |