Von Neumann Algebras for Abstract Harmonic Analysis

von Neumann algebras;abstract harmonic analysis;Fourier algebra;standard form;Pure Mathematics

Zwarich, Cameron

University of Waterloo

关键词: von Neumann algebras;    abstract harmonic analysis;    Fourier algebra;    standard form;    Pure Mathematics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3920/1/thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis develops the theory of operator algebras from the perspective of abstract harmonic analysis, and in particular, the theory of von Neumann algebras. Results from operator algebras are applied to the study of spaces of coefficient functions of unitary representations of locally compact groups, and in particular, the Fourier algebra of a locally compact group. The final result, which requires most of the material developed in earlier sections, is that the group von Neumann algebra of a locally compact group is in standard form.