Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Theotokatos Konstantinos-Panagiotis
Supervisors info:
Αριστείδης Κατάβολος, Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, ΕΚΠΑ
Original Title:
The Fourier and Fourier-Stieltjes algebras of a locally compact group
Translated title:
The Fourier and Fourier-Stieltjes algebras of a locally compact group
Summary:
In this thesis, we define the Fourier and Fourier-Stieltjes algebras of a locally compact group and explore some of their properties. After defining the functions of positive type on a locally compact group G, we will define the Fourier-Stieltjes algebra of G, denoted by B(G), as the linear span of the functions of positive type. Equipped with pointwise operations and a particular norm, B(G) is a Banach algebra, isometrically isomorphic to the dual of the group C*-algebra, as we will show. The Fourier algebra of G, denoted by A(G), is defined as a special closed ideal of B(G) and we will specify its spectrum and its dual. More specifically, we will show that the spectrum of A(G) is homeomorphic to G and that its dual is isometrically isomorphic to the group von Neumann algebra.
Main subject category:
Science
Keywords:
Fourier algebra, Fourier-Stieltjes algebra, locally compact groups, von Neumann algebras, C*-algebras
