Subdiagonal algebras with the Beurling type invariant subspaces

2019/04/03 by Guoxing Ji, Ji, Guoxing · 1 citation
Mathematics · #46K50 #46L52 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1904.01746

openalex publication_date 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathfrak A be a maximal subdiagonal algebra in a σ-finite von Neumann algebra \mathcal M. If every right invariant subspace of \mathfrak A in the non-commutative Hardy space H² is of Beurling type, then we say \mathfrak A to be type 1. We determine generators of these algebras and consider a Riesz type factorization theorem for the non-commutative H¹ space. We show that the right analytic Toeplitz algebra on the non-commutative Hardy space H^p associated with a type 1 subdiagonal algebra with multiplicity 1 is hereditary reflexive.

Citations

• A Beurling theorem for noncommutative L^p
• Analyticity in Operator Algebras

Cited by

• Interpolation problems in subdiagonal algebras

Related

• Noncommutative H^p spaces associated with type 1 subdiagonal algebras
• On a class of subdiagonal algebras
• Riesz and Szegö type factorizations for noncommutative Hardy spaces
• On Haagerup noncommutative quasi H^p(\A) spaces
• A Beurling-Blecher-Labuschagne theorem for Haagerup noncommutative L^p spaces