On positive transitive operators (Q1007113)
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scientific article; zbMATH DE number 5534437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On positive transitive operators |
scientific article; zbMATH DE number 5534437 |
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On positive transitive operators (English)
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27 March 2009
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An operator is called transitive if it does not have any nontrivial invariant subspaces. In [J.~Funct.\ Anal.\ 256, No.\,6, 1865--1874 (2009; Zbl 1162.47006)], the author constructed a transitive operator \(T\) (on \(\ell_1\)) which is almost positive, in the sense that all but one entries in the matrix of the operator are non-negative. In the present paper, it is shown that no operator similar to a translation of \(T\) can be positive.
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invariant subspace
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positive operator
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transitive operator
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