On noncommutative weak Orlicz-Hardy spaces

Bekjan, Turdebek N.; Raikhan, Madi

doi:10.48550/arxiv.2109.07474

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Noncommutative Weak Orlicz Spaces Associated With a Weight1

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2022

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“…In [10], the noncommutative weak Orlicz spaces associated with a weight has been defined for N-function and gave its some properties. Next, we extend it for the growth function case.…”

Section: Noncommutative Weak Orlicz Spaces Associated With a Weightmentioning

confidence: 99%

Haagerup noncommutative Orlicz spaces

Bekjan¹

2022

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Let 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.

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“…In [10], the noncommutative weak Orlicz spaces associated with a weight has been defined for N-function and gave its some properties. Next, we extend it for the growth function case.…”

Section: Noncommutative Weak Orlicz Spaces Associated With a Weightmentioning

confidence: 99%