Volterra semigroups have invariant subspaces (Q1283030)
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scientific article; zbMATH DE number 1274802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Volterra semigroups have invariant subspaces |
scientific article; zbMATH DE number 1274802 |
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Volterra semigroups have invariant subspaces (English)
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17 September 1999
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The article is devoted to the solution of the Volterra semigroup problem. This problem was raised by \textit{E. Nordgren, H. Radjavi} and \textit{P. Rosenthal} [Indiana Univ. Math. J. 33, 271-275 (1984; Zbl 0579.47041)] and has the following form: does every (multiplicative) semigroup of compact quasinilpotent operators on an infinite dimensional Banach space have a nontrivial invariant subspace? The problem is solved with no additional conditions related to nuclearity, positivity, special spectral behaviour and so on. Some consequences are also considered.
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semigroup of operators
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multiplicative semigroup
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compact quasinilpotent operators
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Volterra semigroup
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Volterra algebra
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triangularizability
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positivity
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spectral behaviour
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0.90945417
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0.89052594
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0.88879776
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0.88272405
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0.8751763
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0.87034506
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