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$C_{\cdot 0}$ -contractions: a Jordan model and lattices of invariant subspaces

Author(s): M. F. Gamal'
Translated by: V. V. Kapustin
Original publication: Algebra i Analiz, tom 15 (2003), vypusk 5.
Journal: St. Petersburg Math. J. 15 (2004), 773-793.
MSC (2000): Primary 47A15, 47A45
Posted: July 29, 2004
MathSciNet review: 2068794
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Abstract | References | Similar articles | Additional information

Abstract: A subclass $C_{\cdot 0}(C_0(P), \mathrm{fin})$ of the class of $C_{\cdot 0}$ -contractions is introduced and studied. This subclass is a generalization of the subclass of $C_{\cdot 0}$ -contractions with finite defect indices, and it includes the $C_{\cdot 0}$ -contractions for which $\operatorname{dim}{ \operatorname{Ker}{T^\ast}}\allowbreak <\infty$ and the defect operator $(I-T^\ast T)^{1/2}$ belongs to the Hilbert-Schmidt class. For an operator of class $C_{\cdot 0}(C_0(P), \mathrm{fin})$ , a Jordan model is constructed, and it is proved that the lattices of invariant subspaces remain isomorphic under the quasiaffine transformations.

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