A metric characterization of freeness

摘要

Let M be a finite von Neumann algebra and u1, . . . , uN be unitaries in M. We show that u(1), . . . , u(N) freely generate L(F-N) if and only if sigma(N)(i=1) ui circle times (u(i)(op)) lowast; + u(i ) lowast;circle times u(i)(op) M circle times M-op = 2 root 2N - 1. (C) 2022 Elsevier Inc. All rights reserved.