AMENABLE FOURIER ALGEBRA FROM A CONSTRUCTIBLE GROUP
Keywords:
Fourier Algebra, Fourier transform, constructible group, AmenabilityAbstract
The subject of amenability of Fourier algebra has been a subject of research for decades. It is generally known that Fourier algebras are not generally amenable even though they are operator amenable. In this study we are able to construct an amenable group ???????? . The group has some features including a contractible identity. Its group algebra ???????? (???????? ) is amenable following Barry Johnson’s result. The Fourier algebra is obtained ????(???????? ) is obtained by the actions of Fourier Transforms on ???????? (???????? ), with ???????? as an underlying group. ????(???????? ) inherited the norm from its group algebra ???????? (???????? ). Further, the amenability of ????(???????? ) is obtained and studied. Some groups are paradoxical and non-amenable. The problems of non-amenability posed by these groups have given rise to non-amenable Fourier algebras. This brings some limitations to the study of these algebras which have much of applications in quantum mechanics. Various aspects of amenability and operator amenability can be studied under this Fourier algebra.
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