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Shift-type invariant subspaces of contractions
- Source :
-
Journal of Functional Analysis . May2007, Vol. 246 Issue 2, p281-301. 21p. - Publication Year :
- 2007
-
Abstract
- Abstract: Using the Sz.-Nagy–Foias functional model it was shown in [L. Kérchy, Injection of unilateral shifts into contractions with non-vanishing unitary asymptotes, Acta Sci. Math. (Szeged) 61 (1995) 443–476] that under certain conditions on a contraction T the natural embedding of a Hardy space of vector-valued functions into the corresponding space can be factored into the product of two transformations, intertwining T with a unilateral shift and with an absolutely continuous unitary operator, respectively. The norm estimates in the Factorization Theorem of this paper are sharpened to their best possible form by essential improvements in the proof. As a consequence we obtain that if the residual set of a contraction covers the whole unit circle then those invariant subspaces, where the restriction is similar to the unilateral shift with a similarity constant arbitrarily close to 1, span the whole space. Furthermore, the hyperinvariant subspace problem for asymptotically non-vanishing contractions is reduced to these special circumstances. [Copyright &y& Elsevier]
- Subjects :
- *FUNCTIONAL analysis
*HILBERT space
*MATHEMATICS
*OPERATOR theory
Subjects
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 246
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 24782607
- Full Text :
- https://doi.org/10.1016/j.jfa.2007.01.011