International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 4, Pages 223-230
Proper contractions and invariant subspaces
1Catholic University of Rio de Janeiro, Rio de Janeiro 22453-900, RJ, Brazil
2University of California at Los Angeles, Los Angeles 90024-1594, CA, USA
Received 4 December 2000
Copyright © 2001 C. S. Kubrusly and N. Levan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a contraction and the strong limit of . We prove the following theorem: if a hyponormal contraction does not have a nontrivial invariant subspace, then is either a proper contraction of class or a nonstrict proper contraction of class for which is a completely nonprojective nonstrict proper contraction. Moreover,
its self-commutator is a strict contraction.