Operator-valued Khintchine inequality for $\hat{I}\mu$-free semicircles

Abstract

We exhibit several bounds for operator norms of the sum of $\hat{I}\mu$-free semicircular random variables introduced in the paper of Speicher and Wysoczański. In particular, using the first and second largest eigenvalues of the adjacency matrix $\hat{I}\mu$, we show analogs of the operator-valued Khintchine-type inequality obtained by Haagerup and Pisier.

12 pages and 1 figure. We added new bounds. This version has been accepted for publication with the Bulletin of the London Mathematical Society