Resolvents of R-Diagonal Operators

Details Resolvents of R-Diagonal Operators Resolvents of R-Diagonal Operators

2008-11-19

arxiv.org/abs/0811.3125v1

Mathematics

Operator Algebras

29 pages, 12 figures, used gastex.sty

Scientific paper

We consider the resolvent $(\lambda-a)^{-1}$ of any $R$-diagonal operator $a$ in a $\mathrm{II}_1$-factor. Our main theorem gives a universal asymptotic formula for the norm of such a resolvent. En route to its proof, we calculate the $R$-transform of the operator $|\lambda-c|^2$ where $c$ is Voiculescu's circular operator, and give an asymptotic formula for the negative moments of $|\lambda-a|^2$ for any $R$-diagonal $a$. We use a mixture of complex analytic and combinatorial techniques, each giving finer information where the other can give only coarse detail. In particular, we introduce {\em partition structure diagrams}, a new combinatorial structure arising in free probability.

Affiliated with

Also associated with

No associations

Rating

Resolvents of R-Diagonal Operators 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 Resolvents of R-Diagonal Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Resolvents of R-Diagonal Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-429284