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

Zhang, Xia; Guo, Tiexin

Front. Math. China 6, No. 5, 965-985 (2011).

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.

Reviewer: Anatolij M. Plichko (Krakow)

MSC:

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

Keywords:

random inner product module; random normed module; random unitary operator; random continuous operator; von Neumann’s mean ergodic theorem

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