Invariant Subspaces for Operators in a General II_1-factor

Details Invariant Subspaces for Operators in a General II_1-factor Invariant Subspaces for Operators in a General II_1-factor

2006-11-09

arxiv.org/abs/math/0611256v1

Mathematics

Operator Algebras

83 pages

Scientific paper

It is shown that to every operator T in a general von Neumann factor M of type II_1 and to every Borel set B in the complex plane, one can associate a largest, closed, T-invariant subspace, K = K_T(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 (1-P_K)T|_(1-P_K)(H) is concentrated on C\B. In particular, if T has a Brown measure which is not concentrated on a singleton, then there exists a non-trivial, closed, T-hyperinvariant subspace. Furthermore, it is shown that for every T in M, the limit A=\lim_{n\to\infty}[(T^n)* T^n]^{1/2n} exists in the strong operator topology and K_T(\bar{B(0,r)})=1_{[0,r]}(A), r>0.

Affiliated with

Also associated with

No associations

Rating

Invariant Subspaces for Operators in a General II_1-factor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant Subspaces for Operators in a General II_1-factor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant Subspaces for Operators in a General II_1-factor will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407811