Remarks on a recent result by Paul Skoufranis

Details Remarks on a recent result by Paul Skoufranis Remarks on a recent result by Paul Skoufranis

2012-03-14

arxiv.org/abs/1203.3186v1

Mathematics

Operator Algebras

Scientific paper

We give a different proof of Paul Skoufranis's very recent result showing that the strong convergence of possibly non-commutative random variables $X^{(k)}\to X$ is stable under reduced free product with a fixed non-commutative random variable $Y$. In fact we obtain a more general fact: assuming that the families $X^{(k)}={X_i^{(k)}}$ and $Y^{(k)}={Y_j^{(k)}}$ are *-free as well as their limits (in moments) $X ={X_i}$ and $Y ={Y_j}$, the strong convergences $X^{(k)}\to X$ and $Y^{(k)}\to Y$ imply that of ${X^{(k)},Y^{(k)}}$ to ${X,Y}$. Phrased in more striking language: the reduced free product is "continuous" with respect to strong convergence. The analogue for weak convergence (i.e. convergence of all moments) is obvious.

Affiliated with

Also associated with

No associations

Rating

Remarks on a recent result by Paul Skoufranis 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 Remarks on a recent result by Paul Skoufranis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Remarks on a recent result by Paul Skoufranis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-716235