A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms

<p>We prove Beurling-type theorems for H-invariant spaces in relation to a semifinite von Neu-mann algebra M with a semifinite, faithful, normal tracial weight &tau;, using an extension of Arveson’s non-commutative Hardy space H-. First we prove a Beurling-Blecher-Labuschagne theorem for H-invariant subspaces of L p (M,&tau;) when 0 < p ≤ -. We also prove a Beurling-Chen-Hadwin-Shen theorem for H -invariant subspaces of L a (M,&tau;) where a is a unitarily invariant, locally k 1 -dominating, mutually continuous norm with respect to &\tau;. For a crossed product of a von Neumann algebra M by an action &beta;, M o &beta; Z, we are able to completely characterize all H-invariant subspaces of L a (Mo &beta; Z,t) using our results. As an example, we completely characterize all H-invariant subspaces of the Schatten p-class, S p (H) (0 < p ≤ -), where H - is the lower tri-angular subalgebra of B(H). We also characterize the non-commutative Hardy space H -invariant subspaces in a Banach function space I(&tau;) on a semifinite von Neumann algebra M.</p>

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Dissertation

Year

2017

Author dc:creator

• Sager, Lauren Beth Meitzler

Contributors dc:contributor

• Junhao Shen
• Donald Hadwin
• Karen Graham

• Functional Analysis
• Hardy space
• invariant subspace
• Operator Theory
• semifinite
• von Neumann algebra
• Mathematics

Repository record dc:identifier

https://scholars.unh.edu/dissertation/143

OAI identifier oai:identifier

oai:scholars.unh.edu:dissertation-1142