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Cím:On the residual parts of completely non-unitary contractions.
Szerző:K\'erchy, L.
Forrás:Acta Math. Hung. 50, 127-145 (1987).
Absztrakt:Based on the Sz.-Nagy-Foia\c{s} functional model for completely non- unitary (c.n.u.) contractions on a separable Hilbert space, this paper gives a systematic study of the residual and *-residual parts of such contractions, and proves the reflexivity of certain $C\sb{11}$ contractions. \par To be more precise, recall that the residual part R on space K of a c.n.u. contraction T on H is the unitary part in the Wold decomposition of the minimal isometric dilation of T; the *-residual part $R\sb*$ on $K\sb*$ is similarly defined in terms of $T\sp*$. The paper starts by giving a representation for $R\sb*$ in the functional model of T, and then considers a canonical operator X intertwining T and $R\sb*$ and Y intertwining R and T. Here X (resp. Y) is the restriction to H (resp. K) of the orthogonal projection onto $K\sb*$ (resp. H). The author studies various properties of X and Y such as when they are injective or have dense range, and relates these to properties of T. Samples: X is injective if and only if T can be mapped injectively into some unitary operator; Y has dense range if and only if some unitary operator can be mapped, with dense range, into T. Then the author defines the class of $quasi$-C${}\sb{11}$ contractions, shows by an example that they properly contain $C\sb{11}$ contractions, and concludes the paper by proving two reflexivity results, one for $quasi$-C${}\sb{11}$ contractions and one for $C\sb{11}$ contractions, under certain extra conditions.} \RV{Wu Pei Yuan 
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