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Cím:A description of invariant subspaces of $C\sb{11}$-contractions.
Szerző:K\'erchy, L.
Forrás:J. Oper. Theory 15, 327-344 (1986).
Absztrakt:B.Sz.-Nagy and C. Foia\c{s} have given a description of invariant subspaces of completely nonunitary contractions in terms of regular factorizations of their characteristic function. Since it is rather difficult to look over all regular factorizations of a contractive analytic function even in the simplest cases {\it S. O. Sickler} [Indiana Univ. Math. J. 24, 635-650 (1975; Zbl 0374.47002)] initiated to derive more explicit descriptions of invariant subspaces. His result concerns $C\sb{11}$-contractions with scalar-valued characteristic function, and has been generalized by {\it P. Y. Wu} [J. Oper. Theory 1, 261-272 (1979; Zbl 0431.47007)] to $C\sb{11}$-contractions with a finite matrix characteristic function. Extending these investigations the present paper provides a characterization of the hyperinvariant subspaces of arbitrary $C\sb{11}$-contractions, describes the biinvariant subspaces of $C\sb{11}$-contractions which are weakly similar to unitaries, and gives a description of all invariant subspaces of those contractions whose characteristic function has a scalar multiple. These results are achieved by studying the connection of a $C\sb{11}$-contraction to the attached canonical unitary operator. 
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