Almost periodic functionals and finite-dimensional representations
Tom 243 / 2018
Studia Mathematica 243 (2018), 329-344
MSC: 46H15, 43A60, 43A20, 22D10, 22D20.
DOI: 10.4064/sm170626-26-9
Opublikowany online: 7 May 2018
Streszczenie
We show that if is a C^*-algebra and \lambda \in A^* is a nonzero almost periodic functional which is a coordinate functional of a topologically irreducible involutive representation \pi , then \dim\pi \lt \infty . We introduce the RFD transform \alpha _A : A \rightarrow U(A) of a Banach algebra A and establish its universal property. We show that if A has a bounded two-sided approximate identity, then almost periodic functionals on A which are limits of coordinate functionals of finite-dimensional representations have lifts to almost periodic functionals on U(A). Other connections with almost periodicity and harmonic analysis are also discussed.
