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.

• Subjects / Keywords

  • Adapted probability measure
  • Fourier algebra
  • Group von neumann algebras

• Graduation date

  Fall 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R31J97K0M

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.