Proper contractions and invariant subspaces
Let T be a contraction and A the strong limit of {T∗nTn}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 𝒞00 or a nonstrict proper contraction of class 𝒞10 for which A is a completely nonp...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006287 |
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| author | C. S. Kubrusly N. Levan |
| author_facet | C. S. Kubrusly N. Levan |
| author_sort | C. S. Kubrusly |
| collection | DOAJ |
| description | Let T be a contraction and A the strong limit of {T∗nTn}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 𝒞00 or a nonstrict proper contraction of class 𝒞10 for which A is a completely nonprojective nonstrict proper contraction. Moreover,
its self-commutator [T*,T] is a strict contraction. |
| format | Article |
| id | doaj-art-e18c65cafc354071864a19acd6423e0b |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e18c65cafc354071864a19acd6423e0b2025-08-20T03:20:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0128422323010.1155/S0161171201006287Proper contractions and invariant subspacesC. S. Kubrusly0N. Levan1Catholic University of Rio de Janeiro, Rio de Janeiro, RJ 22453-900, BrazilUniversity of California at Los Angeles, Los Angeles, CA 90024-1594, USALet T be a contraction and A the strong limit of {T∗nTn}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 𝒞00 or a nonstrict proper contraction of class 𝒞10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T*,T] is a strict contraction.http://dx.doi.org/10.1155/S0161171201006287 |
| spellingShingle | C. S. Kubrusly N. Levan Proper contractions and invariant subspaces International Journal of Mathematics and Mathematical Sciences |
| title | Proper contractions and invariant subspaces |
| title_full | Proper contractions and invariant subspaces |
| title_fullStr | Proper contractions and invariant subspaces |
| title_full_unstemmed | Proper contractions and invariant subspaces |
| title_short | Proper contractions and invariant subspaces |
| title_sort | proper contractions and invariant subspaces |
| url | http://dx.doi.org/10.1155/S0161171201006287 |
| work_keys_str_mv | AT cskubrusly propercontractionsandinvariantsubspaces AT nlevan propercontractionsandinvariantsubspaces |