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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.

47A35Ergodic theory of linear operators
46H25Normed modules and Banach modules, topological modules
46C50Generalizations of inner products
47B80Random operators (linear)
60G57Random measures
Full Text: DOI
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