Separation properties and the group von Neumann algebra

  • Author / Creator
    Tanko, Zsolt
  • A group endowed with a topology compatible with the group operations and for which every point has a neighborhood contained in a compact set is called a locally compact group. On such groups, there is a canonical translation invariant Borel measure that one may use to define spaces of p-integrable functions. With this structure at hand, abstract harmonic analysis further associates to a locally compact group various algebras of functions and operators. We study the capacity these algebras to distinguish closed subgroups of a locally compact group. We also characterize an operator algebraic property of von Neumann algebras associated to a locally compact group. Our investigations lead to a concise argument characterizing cyclicity of the left regular representation of a locally compact group.

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  • Type of Item
  • Degree
    Master of Science
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