Model Theory and the mean ergodic theorem for abelian unitary actions

2014/09/22 by Eduardo Duéñez, Dueñez, Eduardo, José Iovino +1
Mathematics · #03C20 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #Primary 03C98 #Secondary 37A30

paper · pdf · doi:10.48550/arxiv.1409.6208

openalex publication_date 2014/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explore connections between von Neumann's mean ergodic theorem and concepts of model theory. As an application we present a proof Wiener's generalization of von Neumann's result in which the group acting on the Hilbert space H is any abelian group of unitary transformations of H.

Related

• A mean ergodic theorem in von-Neumann algebras
• Groupoid approach to the dynamical system of commutative von Neumann Algebras
• Model Theory of General von Neumann Algebras II: Group Actions and Crossed Products
• Mean Ergodic Theorems in Hilbert-Kaplansky spaces
• Ergodic Theorems for coset spaces