Von Neumann’s mean ergodic theorem on complete random inner product modules. (English) Zbl 1235.47015

The authors continue investigations of T.Guo and his coauthors on random normed (and inner product) modules. The inner product module is a linear space \(S\) with a mapping \(\langle\cdot,\cdot \rangle\) from \(S\times S\) into a space \(L^0\) of all measurable functions on a probability space, with natural axioms. The authors prove two forms of von Neumann’s mean ergodic theorem within the framework of complete random inner product modules, and present some applications.


47A35 Ergodic theory of linear operators
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.)
47B80 Random linear operators
60G57 Random measures
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