Rademacher averages on noncommutative symmetric spaces

Details Rademacher averages on noncommutative symmetric spaces Rademacher averages on noncommutative symmetric spaces

2008-03-31

arxiv.org/abs/0803.4404v1

Mathematics

Operator Algebras

Scientific paper

Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let $(\epsilon_k)_k$ be a Rademacher sequence, on some probability space $\Omega$. For finite sequences $(x_k)_k of E(M), we consider the Rademacher averages $\sum_k \epsilon_k\otimes x_k$ as elements of the noncommutative function space $E(L^\infty(\Omega)\otimes M)$ and study estimates for their norms $\Vert \sum_k \epsilon_k \otimes x_k\Vert_E$ calculated in that space. We establish general Khintchine type inequalities in this context. Then we show that if E is 2-concave, the latter norm is equivalent to the infimum of $\Vert (\sum y_k^*y_k)^{{1/2}}\Vert + \Vert (\sum z_k z_k^*)^{{1/2}}\Vert$ over all $y_k,z_k$ in E(M) such that $x_k=y_k+z_k$ for any k. Dual estimates are given when E is 2-convex and has a non trivial upper Boyd index. We also study Rademacher averages for doubly indexed families of E(M).

Affiliated with

Also associated with

No associations

Rating

Rademacher averages on noncommutative symmetric spaces 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 Rademacher averages on noncommutative symmetric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rademacher averages on noncommutative symmetric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-197182