On Uniform Equicontinuity of Sequences of Measurable Operators

2010/12/15 by Semyon Litvinov, Litvinov, Semyon
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1012.3425

There is an error in the proof of a critical statement

arxiv created 2014/05/17 · arxiv updated 2014/05/20

Abstract

The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform equicontinuity in measure at zero on a dense subset implies the uniform equicontinuity on the entire space, which is then applied to derive some non-commutative ergodic theorems

Related

• Local ergodic theorems in symmetric spaces of measurable operators
• A note on equicontinuity of families of operators and automorphisms
• Notes on noncommutative ergodic theorems
• Individual ergodic theorems for semifinite von Neumann algebras
• Inequalities for trace on τ-measurable operators