Proper contractions and invariant subspaces

C. S. Kubrusly and N. Levan

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 28, 1-8

Abstract:

Let T be a contraction and A the strong limit of { T ∗ n T n } n ≥ 1 . We prove the following theorem: if a hyponormal contraction T does not have a nontrivial invariant subspace, then T is either a proper contraction of class 𝒞 00 or a nonstrict proper contraction of class 𝒞 10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [ T * , T ] is a strict contraction.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:946042

DOI: 10.1155/S0161171201006287

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