2024/02/14 by Raúl Quiroga-Barranco, Quiroga-Barranco, Raul
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Mathematics and Applications #Operator Algebras (math.OA) #Primary 46L10 #Rough Sets and Fuzzy Logic #Secondary 46L35
paper · pdf · doi:10.48550/arxiv.2402.09601
openalex publication_date 2024/02/14 · openalex created_date 2024/02/18 · openalex updated_date 2026/07/28
We study the relationship between operator algebras, C^* and von Neumann, acting on a Hilbert space and unitary representations of topological groups on the same space. We obtain certain correspondences between both these families of objects. In particular, we prove that the study of Abelian subalgebras of a norm-separable C^*-algebra can be, in many aspects, reduced to the study of unitary representations of Polish groups. It is shown that our techniques have applications to the construction and classification of Abelian subalgebras of operator C^*-algebras on separable Hilbert spaces.