{"id":{"repo_id":"unh-thes","oai_identifier":"oai:scholars.unh.edu:dissertation-1142"},"canonical_url":"https://search.dev.ndltd.org/etd/unh-thes/oai:scholars.unh.edu:dissertation-1142","repository":{"repo_id":"unh-thes","name":"University of New Hampshire","base_url":"https://scholars.unh.edu/do/oai/"},"display":{"title":"A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms","abstract":"<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>","abstract_html":"&lt;p&gt;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 &amp;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,&amp;tau;) when 0 &lt; p ≤ -. We also prove a Beurling-Chen-Hadwin-Shen theorem for H -invariant subspaces of L a (M,&amp;tau;) where a is a unitarily invariant, locally k 1 -dominating, mutually continuous norm with respect to &amp;\\tau;. For a crossed product of a von Neumann algebra M by an action &amp;beta;, M o &amp;beta; Z, we are able to completely characterize all H-invariant subspaces of L a (Mo &amp;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 &lt; 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(&amp;tau;) on a semifinite von Neumann algebra M.&lt;/p&gt;","abstract_has_math":false,"creators":["Sager, Lauren Beth Meitzler"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Junhao Shen","Donald Hadwin","Karen Graham"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-01-01T08:00:00Z","date_published":"2017-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:01Z","subjects":["Functional Analysis","Hardy space","invariant subspace","Operator Theory","semifinite","von Neumann algebra","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/143","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Junhao Shen","Donald Hadwin","Karen Graham"]},{"key":"dc:creator","label":"Author","values":["Sager, Lauren Beth Meitzler"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Functional Analysis","Hardy space","invariant subspace","Operator Theory","semifinite","von Neumann algebra","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/143"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<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>"]},{"key":"dc:title","label":"Title","values":["A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms"]}]}],"canonical_facts":{"dc:contributor":["Junhao Shen","Donald Hadwin","Karen Graham"],"dc:creator":["Sager, Lauren Beth Meitzler"],"dc:description.abstract":["<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>"],"dc:identifier":["https://scholars.unh.edu/dissertation/143"],"dc:subject":["Functional Analysis","Hardy space","invariant subspace","Operator Theory","semifinite","von Neumann algebra","Mathematics"],"dc:title":["A Beurling Theorem for Noncommutative Hardy Spaces Associated with a Semifinite von Neumann Algebra with Various Norms"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:22:01Z"}