Proper Contractions and Invariant Subspaces
نویسندگان
چکیده
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 00 or a nonstrict proper contraction of class 10 for which A is a completely nonprojective nonstrict proper contraction. Moreover, its self-commutator [T∗,T ] is a strict contraction. 2000 Mathematics Subject Classification. 47A15, 47B20.
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