The a priori Tan Theta Theorem for spectral subspaces

Details The a priori Tan Theta Theorem for spectral subspaces The a priori Tan Theta Theorem for spectral subspaces

2010-12-07

arxiv.org/abs/1012.1569v2

Mathematics

Spectral Theory

v2: the paper has been rearranged and shortened

Scientific paper

Let A be a self-adjoint operator on a separable Hilbert space H. Assume that the spectrum of A consists of two disjoint components s_0 and s_1 such that the set s_0 lies in a finite gap of the set s_1. Let V be a bounded self-adjoint operator on H off-diagonal with respect to the partition spec(A)=s_0 \cup s_1. It is known that if ||V||<\sqrt{2}d, where d=\dist(s_0,s_1), then the perturbation V does not close the gaps between s_0 and s_1 and the spectrum of the perturbed operator L=A+V consists of two isolated components s'_0 and s'_1 grown from s_0 and s_1, respectively. Furthermore, it is known that if V satisfies the stronger bound ||V||< d then the following sharp norm estimate holds: ||E_L(s'_0)-E_A(s_0)|| \leq sin(arctan(||V||/d)), where E_A(s_0) and E_L(s'_0) are the spectral projections of A and L associated with the spectral sets s_0 and s'_0, respectively. In the present work we prove that this estimate remains valid and sharp also for d \leq ||V||< \sqrt{2}d, which completely settles the issue.

Affiliated with

Also associated with

No associations

Rating

The a priori Tan Theta Theorem for spectral subspaces 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 The a priori Tan Theta Theorem for spectral subspaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The a priori Tan Theta Theorem for spectral subspaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-481251