Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

Search: All articles in the CMB digital archive with keyword strong convergence

  Expand all        Collapse all Results 1 - 1 of 1

1. CMB 2014 (vol 57 pp. 708)

Brannan, Michael
Strong Asymptotic Freeness for Free Orthogonal Quantum Groups
It is known that the normalized standard generators of the free orthogonal quantum group $O_N^+$ converge in distribution to a free semicircular system as $N \to \infty$. In this note, we substantially improve this convergence result by proving that, in addition to distributional convergence, the operator norm of any non-commutative polynomial in the normalized standard generators of $O_N^+$ converges as $N \to \infty$ to the operator norm of the corresponding non-commutative polynomial in a standard free semicircular system. Analogous strong convergence results are obtained for the generators of free unitary quantum groups. As applications of these results, we obtain a matrix-coefficient version of our strong convergence theorem, and we recover a well known $L^2$-$L^\infty$ norm equivalence for non-commutative polynomials in free semicircular systems.

Keywords:quantum groups, free probability, asymptotic free independence, strong convergence, property of rapid decay
Categories:46L54, 20G42, 46L65

© Canadian Mathematical Society, 2014 :