Geometric eigenspace of the generator ofC
0-semigroup of positive operators |
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Authors: | Ruey-Jen Jang |
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Institution: | (1) Department of Mathematics and Statistics, Texas Tech University, 79409-1042 Lubbock, Texas, USA |
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Abstract: | LetE be a Banach lattice with order continuous norm and {T(t)}
t0 be an eventually compactc
0-semigroup of positive operators onE 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 element ofE with certain positivity structure. This is achieved by a decomposition of the underlying Banach latticeE into a direct sum of closed ideals which can be viewed as a generalization of the Frobenius normal form for nonnegative reducible matrices. |
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Keywords: | 47B60 47B65 47D03 |
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