Invariant sublattices for positive operators |
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Authors: | AK Kitover |
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Institution: | a Department ofMathematics, Philadelphia Community College, USA b Department of Pure Mathematics, Queens University Belfast, Northern Ireland |
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Abstract: | There are, by now, many results which guarantee that positive operators on Banach lattices have non-trivial closed invariant sublattices. In particular, this is true for every positive compact operator. Apart from some results of a general nature, in this paper we present several examples of positive operators on Banach lattices which do not have non-trivial closed invariant sublattices. These examples include both AM-spaces and Banach lattices with an order continuous norm and which are and are not atomic. In all these cases we can ensure that the operators do possess non-trivial closed invariant subspaces. |
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Keywords: | Banach lattices Positive operators Invariant sublattice |
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