Year: 2022
Type: preprint
Abstract: Let $\mathcal{M}$ be a $σ$-finite von Neumann algebra equipped with a normal faithful state $φ$, and let $Φ$ be a growth function. We consider Haagerup noncommutative Orlicz spaces $L^Φ(\M,φ)$ associated with $\M$ and $φ$, which are analogues of Haagerup $L^p$-spaces. We show that $L^Φ(\M,φ)$ is independent of $φ$ 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.
Source: arXiv (Cornell University)
Author: Bekjan, Turdebek N.
Institution: Astana IT University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4296544691