Haagerup noncommutative Orlicz spaces

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra equipped with a normal faithful state $\varphi$, and let $\Phi$ be a growth function. We consider Haagerup noncommutative Orlicz spaces L^\Phi(\M,\varphi) associated with \M and $\varphi$, which are analogues of Haagerup $L^p$-spaces. We show that L^\Phi(\M,\varphi) is independent of $\varphi$ 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.Comment: 4

Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales

We prove that atomic decomposition for the Hardy spaces h_1 and H_1 is valid for noncommutative martingales. We also establish that the conditioned Hardy spaces of noncommutative martingales h_p and bmo form interpolation scales with respect to both complex and real interpolations

Interpolation of Haagerup noncommutative Hardy spaces

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal algebra of $\mathcal{M}$. We prove Stein-Weiss type interpolation theorem of Haagerup noncommutative $H^{p}$-spaces associated with \A.Comment: 16. arXiv admin note: text overlap with arXiv:2209.0854

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