2023/08/26 by Panchugopal Bikram, Bikram, Panchugopal, Diptesh Saha +1
Mathematics · Economics, Econometrics and Finance · #Advanced Operator Algebra Research #Advanced Banach Space Theory #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2308.13907
In this article, we prove Neveu decomposition for the action of the locally compact amenable semigroup of positive contractions on semifinite von Neumann algebras and thus, it entirely resolves the problem for the actions of arbitrary amenable semigroup on semifinite von Neumann algebras. We also prove it for amenable group actions by Markov automorphisms on any σ-finite von Neumann algebras. As an application, we obtain stochastic ergodic theorem for actions of ℤ+d and ℝ+d for d ∈ ℕ by positive contractions on L1-spaces associated with a finite von Neumann algebra. It yields the first ergodic theorem for positive contraction on non-commutative L1-spaces beyond the Danford-Schwartz category.