论文标题
haagerup非交换性orlicz空间
Haagerup noncommutative Orlicz spaces
论文作者
论文摘要
令$ \ Mathcal {M} $为$σ$ -Finite von Neumann代数，配备了正常的忠实状态$φ$，让$φ$为增长功能。我们认为与$ \ m $和$φ$相关的haagerup noncolup orlicz空间$ l^φ（\ m，φ）$，它们是Haagerup $ l^p $ -spaces的类似物。我们表明，$ l^φ（\ m，φ）$独立于$φ$，而同构同构。我们证明了Haagerup的减少定理和该空间的二元定理。随着这些结果的应用，我们将奇异案例中的一些非交换性martingale不平等扩展到Haagerup非交换性Orlicz空间案例。
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.
