Haagerup noncommutative Orlicz spaces
Turdebek N. Bekjan

TL;DR
This paper introduces Haagerup noncommutative Orlicz spaces associated with von Neumann algebras, proving their key properties and extending noncommutative martingale inequalities beyond the tracial setting.
Contribution
It establishes the independence of these spaces from the state, proves fundamental theorems like Haagerup's reduction and duality, and extends martingale inequalities to this new context.
Findings
Spaces are independent of the chosen state up to isometry
Proved Haagerup's reduction and duality theorems for these spaces
Extended noncommutative martingale inequalities to the Orlicz space setting
Abstract
Let be a -finite von Neumann algebra equipped with a normal faithful state , and let be a growth function. We consider Haagerup noncommutative Orlicz spaces associated with and , which are analogues of Haagerup -spaces. We show that is independent of up to isometric isomorphism. We prove the Haagerup's reduction theorem and the duality theorem for this spaces. As application of these results, we extend some noncommutative martingale inequalities in the tracial case to the Haagerup noncommutative Orlicz space case.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory
