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## Studia Mathematica

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## 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 $A$ 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.

#### Autorzy

• M. FilaliDepartment of Mathematical Sciences
University of Oulu
Oulu 90014, Finland
e-mail
• M. Sangani MonfaredDepartment of Mathematics and Statistics
University of Windsor
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