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Lomonosov's hyperinvariant subspace theorem for real spaces

Published online by Cambridge University Press:  24 October 2008

N. D. Hooker
N. D. Hooker
Affiliation:
St John's College, Cambridge
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Extract

In 1973, V.I.Lomonosov introduced a new technique for finding invariant and hyperinvariant subspaces for certain classes of (continuous, linear) operators on complex Banach spaces. Recall that a closed subspace M of the Banach space X is called hyperinvariant for the operator T if S(M) ⊂ M for every operator S which commutes with T.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 129 - 133
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

(1)Daughtry, J.An invariant subspace theorem. Proc. Amer. Math. Soc. 49 (1975), 267–268.Google Scholar
(2)Kim, H. W., Pearcy, C. M. and Shields, A. L.Rank-one commutators and hyperinvariant subspaces. Michigan Math. J. 22 (1975), 193–194.Google Scholar
(3)Landsberg, M. and Pech, G.Hyperinvariante Teilräume stetiger Abbildungen in topologischer Vektorräumen. J. Reine Angew. Math. 293 (1977), 253–262.Google Scholar
(4)Pearcy, C. M. and Shields, A. L. A survey of the Lomonosov technique in the theory of invariant subspaces. Topics in operator theory. Amer. Math. Soc. Surveys no. 13, Providence R.I., 1974.CrossRefGoogle Scholar
(5)Williamson, J. H.Compact linear operators in linear topological spaces. J. London Math. Soc. 29 (1954), 149–156.CrossRefGoogle Scholar