# Kérchy László honlapja

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Vissza.

 Cím: On the residual parts of completely non-unitary contractions. Szerzõ: K\'erchy, L. Forrás: Acta Math. Hung. 50, 127-145 (1987). Nyelv: English 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 Letöltés: | Zentralblatt