Strong convergence for reduced free products Academic Article

abstract

• Using an inequality due to Ricard and Xu, we give a different proof of Paul Skoufraniss recent result showing that the strong convergence of possibly non-commutative random variables [Formula: see text] is stable under reduced free product with a fixed non-commutative random variable [Formula: see text]. In fact we obtain a more general fact: assuming that the families [Formula: see text] and [Formula: see text] are -free as well as their limits (in moments) [Formula: see text] and [Formula: see text], the strong convergences [Formula: see text] and [Formula: see text] imply that of [Formula: see text] to [Formula: see text]. 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. Our approach extends to the amalgamated free product, left open by Skoufranis.

authors

• Pisier, Gilles

published proceedings

• INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS

author list (cited authors)

• Pisier, G.

citation count

• 0

complete list of authors

• Pisier, Gilles

publication date

• June 2016

publisher

• World Scientific Publishing  Publisher

published in

• Infinite Dimensional Analysis Quantum Probability and Related Topics  Journal

keywords

• Non-commutative Khintchine Inequality
• Reduced Amalgamated Free Product
• Reduced Free Product
• Strong Convergence

Digital Object Identifier (DOI)

• 10.1142/S0219025716500089

start page

• 1650008

end page

• 1650008

volume

• 19

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1142%2Fs0219025716500089