Invariant Subspaces for Operators in a General II1-factor
نویسندگان
چکیده
It is shown that to every operator T in a general von Neumann factor M of type II1 and to every Borel set B in the complex plane C, one can associate a maximal, closed, T -invariant subspace, K = KT (B), affiliated with M, such that the Brown measure of T |K is concentrated on B. Moreover, K is T -hyperinvariant, and the Brown measure of PK⊥T |K⊥ is concentrated on C \ B. In particular, if T ∈ M has a Brown measure which is not concentrated on a singleton, then there exists a non-trivial, closed, T -hyperinvariant subspace. This paper substitutes and extends the unplublished manuscript [H1] by the first author, where similar results were proved under the assumption that M embeds in an ultrapower Rω of the hyperfinite II1-factor R.
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