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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Unicellular operators


Authors: José Barría and Kenneth R. Davidson
Journal: Trans. Amer. Math. Soc. 284 (1984), 229-246
MSC: Primary 47A15; Secondary 47A45, 47B37
MathSciNet review: 742423
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Abstract: An operator is unicellular if its lattice of invariant subspaces is totally ordered by inclusion. The list of nests which are known to be the set of invariant subspaces of a unicellular operator is surprisingly short. We construct unicellular operators on $ {l^p},1 \leqslant p < \infty $, and on $ {c_0}$ with lattices isomorphic to $ \alpha + X + {\beta ^{\ast}}$ where $ \alpha $ and $ \beta $ are countable (finite or zero) ordinals, and $ X$ is in this short list. Certain other nests are attained as well.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0742423-2
PII: S 0002-9947(1984)0742423-2
Keywords: Unicellular operator, invariant subspaces, attainable lattices
Article copyright: © Copyright 1984 American Mathematical Society