## Nehari and Carathéodory-Fejér type extension results for operator-valued functions on groups

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- by Mihály Bakonyi
- Proc. Amer. Math. Soc.
**131**(2003), 3517-3525 - DOI: https://doi.org/10.1090/S0002-9939-03-06897-7
- Published electronically: February 20, 2003
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## Abstract:

Let $G$ be a compact abelian group having the property that its character group $\Gamma$ is totally ordered by a semigroup $P$. We prove that every operator-valued function $k$ on $G$ of the form $k(x)=\sum \limits _{\gamma \in (-P)}\gamma (x)k_{\gamma }$, such that the Hankel operator $H_k$ is bounded, has an essentially bounded extension $K$ with $||K||_{\infty }=||H_k||$. The proof is based on Arveson’s Extension Theorem for completely positive functions on $C^*$-algebras. Among the corollaries we have a Carathéodory-Fejér type result for analytic operator-valued functions defined on such groups.## References

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## Bibliographic Information

**Mihály Bakonyi**- Affiliation: Department of Mathematics, Georgia State University, Atlanta, Georgia 30303-3083
- Email: mbakonyi@cs.gsu.edu
- Received by editor(s): March 6, 2002
- Received by editor(s) in revised form: June 16, 2002
- Published electronically: February 20, 2003
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 3517-3525 - MSC (2000): Primary 43A17, 47A57, 43A35, 47A20
- DOI: https://doi.org/10.1090/S0002-9939-03-06897-7
- MathSciNet review: 1991764