On Limit theorems in $JW$- algebras
Abdusalom Karimov, Farrukh Mukhamedov

TL;DR
This paper investigates convergence properties and ergodic theorems in $JW$-algebras, focusing on bundle convergence, conditional expectations, and supermartingale convergence.
Contribution
It introduces new ergodic theorems based on bundle convergence and explores conditional expectations in reversible $JW$-algebras, advancing the understanding of their convergence behavior.
Findings
Proved ergodic theorems with respect to bundle convergence.
Established convergence of supermartingales in $JW$-algebras.
Analyzed conditional expectations in reversible $JW$-algebras.
Abstract
In the present paper, we study bundle convergence in - algebra and prove certain ergodic theorems with respect to such convergence. Moreover, conditional expectations of reversible -algebras are considered. Using such expectations, the convergence of supermartingales in such is established.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Topics in Algebra
