Wiener's inversion theorem for a certain class of $^{*}$-algebras
Volume 137 / 2014
Colloquium Mathematicum 137 (2014), 103-116
MSC: Primary 46K05; Secondary 46K10, 43A25.
DOI: 10.4064/cm137-1-7
Abstract
We generalize Wiener's inversion theorem for Fourier transforms on closed subsets of the dual group of a locally compact abelian group to cosets of ideals in a class of non-commutative $^*$-algebras having specified properties, which are all fulfilled in the case of the group algebra of any locally compact abelian group.
