A Beurling-Chen-Hadwin-Shen Theorem for Noncommutative Hardy Spaces Associated with Semifinite von Neumann Algebras with Unitarily Invariant Norms

2018/01/04 by Lauren Sager, Wenjing Liu, Sager, Lauren +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1801.01448

openalex publication_date 2018/01/04 · openalex created_date 2018/01/12 · openalex updated_date 2026/07/28

Abstract

We introduce a class of unitarily invariant, locally ‖⋅‖₁-dominating, mutually continuous norms with repect to τ on a von Neumann algebra M with a faithful, normal, semifinite tracial weight τ. We prove a Beurling-Chen-Hadwin-Shen theorem for H^∞-invariant spaces of L^α(M,τ), where α is a unitarily invariant, locally ‖⋅‖₁-dominating, mutually continuous norm with respect to τ, and H^∞ is an extension of Arveson's noncommutative Hardy space. We use our main result to characterize the H^∞-invariant subspaces of a noncommutative Banach function space \mathcal I(τ) with the norm ‖⋅‖_E on M, the crossed product of a semifinite von Neumann algebra by an action β, and B(H) for a separable Hilbert space H.

Citations

• Riesz and Szegö type factorizations for noncommutative Hardy spaces
• A Beurling theorem for noncommutative L^p
• On the maximality of subdiagonal algebras
• On two problems concerning linear transformations in hilbert space
• Analyticity in Operator Algebras

Related

• An Extension of the Beurling-Chen-Hadwin-Shen Theorem for Noncommutative Hardy Spaces Associated with Finite von Neumann Algebras
• A Beurling-Blecher-Labuschagne Theorem for noncommutative Hardy spaces associated with semifinite von Neumann algebras
• A non-commutative Beurling's theorem with respect to unitarily invariant norms
• A Generalized Beurling Theorem in Finite von Neumann Algebras
• Notes on noncommutative ergodic theorems