On Transitive Algebras Containing a Standard Finite von Neumann Subalgebra
| Autor: | Junsheng Fang, Mohan Ravichandran, Don Hadwin |
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| Rok vydání: | 2006 |
| Předmět: |
Hyperinvariant subspaces
Pure mathematics n-Fold transitive Tomita–Takesaki theory C*-algebra symbols.namesake Free products FOS: Mathematics Affiliated operator Operator Algebras (math.OA) Mathematics Discrete mathematics Jordan algebra Mathematics::Operator Algebras Subalgebra Mathematics - Operator Algebras Transitive algebras 46L54 47C15 Von Neumann algebra symbols Von Neumann regular ring Brown measures Abelian von Neumann algebra Standard finite von Neumann algebras Analysis Operator ranges |
| DOI: | 10.48550/arxiv.math/0611290 |
| Popis: | Let $\M$ be a finite von Neumann algebra acting on a Hilbert space $\H$ and $\AA$ be a transitive algebra containing $\M'$. In this paper we prove that if $\AA$ is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. This implies that if a transitive algebra containing a standard finite von Neumann algebra (in the sense of [Ha1]) is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. Non-selfadjoint algebras related to free products of finite von Neumann algebras, e.g., $\L{\mathbb{F}_n}$ and $(M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr)$, are studied. Brown measures of certain operators in $(M_2(\cc), {1/2}Tr)*(M_2(\cc), {1/2}Tr)$ are explicitly computed. Comment: 24 pages, to appear on Journal of Functional Analysis |
| Databáze: | OpenAIRE |
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