A mean ergodic theorem of an amenable group action

作者：Mohari Anilesh^*

来源：Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2014, 17(1): 1450003.

DOI：10.1142/S0219025714500039

• Birkhoff
• ergodic
• Kadison-Schwarz
• amenable group

We consider a sequence of weak Kadison-Schwarz maps T-n on a von-Neumann algebra M with a faithful normal state phi sub-invariant for each (T-n, n = 1) and use a duality argument to prove strong convergence of their pre-dual maps when their induced contractive maps (T-n, n = 1) on the GNS space of (M, phi) are strongly convergent. The result is applied to deduce improvements of some known ergodic theorems and Birkhoff's mean ergodic theorem for any locally compact second countable amenable group action on the pre-dual Banach space M-*.

• 出版日期2014-3
• 单位常州工学院