K-closedness results in noncommutative Lebesgue spaces with filtrations

2024/07/17 by Hugues Moyart, Moyart, Hugues
Mathematics · #46B70 (Primary) 46E30 #46L51 #46L52 #46L53 #60G42 #60G48 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2407.12335

openalex publication_date 2024/07/17 · openalex created_date 2024/09/09 · openalex updated_date 2026/08/01

Abstract

In this paper, we establish a new general K-closedness result in the context of real interpolation of noncommutative Lebesgue spaces involving filtrations. As an application, we derive K-closedness results for various classes of noncommutative martingale Hardy spaces, addressing a problem raised by Randrianantoanina. The proof of this general result adapts Bourgain's approach to the real interpolation of classical Hardy spaces on the disk within the framework of noncommutative martingales.

Related

• P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II
• Theory of H_p-spaces for continuous filtrations in von Neumann algebras
• Duality for symmetric Hardy spaces of noncommutative martingales
• Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales
• Gundy's decomposition for non-commutative martingales and applications