I develop the theory of Kadison-Singer algebras, introduced recently by Ge and Yuan. I prove basic structure theorems, construct several new examples and explore connections to other areas of operator algebras. In chapter 1, I survey those aspects of the theory of non-selfadjoint algebras that are relevant to this work. In chapter 2, I define Kadison-Singer algebras and give different proofs of results of Ge-Yuan, which will be further extended in the last chapter. In chapter 3, I analyse in detail a class of elementary Kadison-Singer algebras that contain Hinfinity and describe their lattices of projections. In chapter 4, I use ideas from free probability theory to construct Kadison-Singer algebras with core the free group factors L(Fr) for r < 2. I then introduce two constructions that yield new Kadison-Singer algebras - The maximal join and the minimal join. In chapter 5, I analyse tensor products of Kadison-Singer algebras, showing that they are never Kadison-Singer. I then show how under certain conditions, one may construct a Kadison-Singer algebra with core the tensor product of the core of two given Kadison-Singer algebras.
","abstract_html":"<p>I develop the theory of Kadison-Singer algebras, introduced recently by Ge and Yuan. I prove basic structure theorems, construct several new examples and explore connections to other areas of operator algebras. In chapter 1, I survey those aspects of the theory of non-selfadjoint algebras that are relevant to this work. In chapter 2, I define Kadison-Singer algebras and give different proofs of results of Ge-Yuan, which will be further extended in the last chapter. In chapter 3, I analyse in detail a class of elementary Kadison-Singer algebras that contain Hinfinity and describe their lattices of projections. In chapter 4, I use ideas from free probability theory to construct Kadison-Singer algebras with core the free group factors L(Fr) for r < 2. I then introduce two constructions that yield new Kadison-Singer algebras - The maximal join and the minimal join. In chapter 5, I analyse tensor products of Kadison-Singer algebras, showing that they are never Kadison-Singer. I then show how under certain conditions, one may construct a Kadison-Singer algebra with core the tensor product of the core of two given Kadison-Singer algebras.</p>","abstract_has_math":false,"creators":["Ravichandran, Mohan"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Liming Ge"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-01-01T08:00:00Z","date_published":"2009-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:25Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/501","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Liming Ge"]},{"key":"dc:creator","label":"Author","values":["Ravichandran, Mohan"]}]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/501"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["I develop the theory of Kadison-Singer algebras, introduced recently by Ge and Yuan. I prove basic structure theorems, construct several new examples and explore connections to other areas of operator algebras. In chapter 1, I survey those aspects of the theory of non-selfadjoint algebras that are relevant to this work. In chapter 2, I define Kadison-Singer algebras and give different proofs of results of Ge-Yuan, which will be further extended in the last chapter. In chapter 3, I analyse in detail a class of elementary Kadison-Singer algebras that contain Hinfinity and describe their lattices of projections. In chapter 4, I use ideas from free probability theory to construct Kadison-Singer algebras with core the free group factors L(Fr) for r < 2. I then introduce two constructions that yield new Kadison-Singer algebras - The maximal join and the minimal join. In chapter 5, I analyse tensor products of Kadison-Singer algebras, showing that they are never Kadison-Singer. I then show how under certain conditions, one may construct a Kadison-Singer algebra with core the tensor product of the core of two given Kadison-Singer algebras.
"]},{"key":"dc:title","label":"Title","values":["Kadison -Singer algebras with applications to von Neumann algebras"]}]}],"canonical_facts":{"dc:contributor":["Liming Ge"],"dc:creator":["Ravichandran, Mohan"],"dc:description.abstract":["I develop the theory of Kadison-Singer algebras, introduced recently by Ge and Yuan. I prove basic structure theorems, construct several new examples and explore connections to other areas of operator algebras. In chapter 1, I survey those aspects of the theory of non-selfadjoint algebras that are relevant to this work. In chapter 2, I define Kadison-Singer algebras and give different proofs of results of Ge-Yuan, which will be further extended in the last chapter. In chapter 3, I analyse in detail a class of elementary Kadison-Singer algebras that contain Hinfinity and describe their lattices of projections. In chapter 4, I use ideas from free probability theory to construct Kadison-Singer algebras with core the free group factors L(Fr) for r < 2. I then introduce two constructions that yield new Kadison-Singer algebras - The maximal join and the minimal join. In chapter 5, I analyse tensor products of Kadison-Singer algebras, showing that they are never Kadison-Singer. I then show how under certain conditions, one may construct a Kadison-Singer algebra with core the tensor product of the core of two given Kadison-Singer algebras.
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