Filali, M., Sangani Monfared, M. (2018) Almost periodic functionals and finite-dimensional representations. Studia Mathematica, 243 (3), 329-344. doi:10.4064/sm170626-26-9

### Almost periodic functionals and finite-dimensional representations

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Author: Filali, M.1; Monfared, M. Sangani2
Organizations: 1Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland
2Department of Mathematics and Statistics, University of Windsor, Windsor, ON, N9B 3P4, Canada
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Language: English
Published: Polish Academy of Sciences, Institute of Mathematics, 2018
Publish Date: 2019-04-08
Description:

# Abstract

We show that if $$A$$ is a $$\mathrm{C}^*$$-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.

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Series: Studia mathematica
ISSN: 0039-3223
ISSN-E: 1730-6337
ISSN-L: 0039-3223
Volume: 243
Pages: 329 - 344
DOI: 10.4064/sm170626-26-9