$C_{\cdot 0}$-contractions: a Jordan model and lattices of invariant subspaces
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M. F. Gamal′
Translated by: V. V. Kapustin - St. Petersburg Math. J. 15 (2004), 773-793
- DOI: https://doi.org/10.1090/S1061-0022-04-00831-3
- Published electronically: July 29, 2004
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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 $T$ for which $\operatorname {dim}{ \operatorname {Ker}{T^\ast }}<\infty$ 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.References
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Bibliographic Information
- M. F. Gamal′
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg, 191023, Russia
- Email: gamal@pdmi.ras.ru
- Received by editor(s): March 3, 2003
- Published electronically: July 29, 2004
- Additional Notes: Partially supported by RFBR (grants nos. 02-01-00264 and NSh-2266.2003.1).
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 773-793
- MSC (2000): Primary 47A15, 47A45
- DOI: https://doi.org/10.1090/S1061-0022-04-00831-3
- MathSciNet review: 2068794
Dedicated: Dedicated to the memory of Professor Yuri A. Abramovich