Journal of Operator Theory

Volume 79, Issue 2, Spring 2018 pp. 269-285.

Similarity degree of type II$_{1}$ von Neumann algebras with Property $\Gamma$

Authors: Don Hadwin (1) Wenhua Qian (2) and Junhao Shen (3)
Author institution:(1) Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, U.S.A.
(2) School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
(3) Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, U.S.A.

Summary: In this paper, we discuss some equivalent definitions of Property~$\Gamma$ for a type II$_1$ von Neumann algebra. Using these equivalent definitions, we prove that the Pisier's similarity degree of a type II$_1$ von Neumann algebra with Property $\Gamma$ is equal to $3$.

DOI: http://dx.doi.org/10.7900/jot.2015dec14.2180
Keywords: property $\Gamma$, similarity problem, similarity degree

Contents Full-Text PDF