A Beurling-Blecher-Labuschagne Theorem for noncommutative Hardy spaces associated with semifinite von Neumann algebras

2016/03/05 by Sager, Lauren
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1603.01735

Abstract

In 2008, Blecher and Labuschagne extended Beurling's classical theorem to H^∞-invariant subspaces of L^p(M,τ) for a finite von Neumann algebra M with a finite, faithful, normal tracial state τ when 1≤ p≤ ∞. In this paper, using Arveson's non-commutative Hardy space H^∞ in relation to a von Neumann algebra M with a semifinite, faithful, normal tracial weight τ, we prove a Beurling-Blecher-Labuschagne theorem for H^∞-invariant spaces of L^p(M,τ) when 0

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