Arhippainen, Jorma; Kauppi, Jukka; Mattas, Jussi. Order structure, multipliers, and Gelfand representation of vector-valued function algebras. Banach J. Math. Anal. 11 (2017), no. 1, 207--222. doi:10.1215/17358787-3784682. https://projecteuclid.org/euclid.bjma/1481274115

### Order structure, multipliers, and Gelfand representation of vector-valued function algebras

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Author: Arhippainen, Jorma1; Kauppi, Jukka1; Mattas, Jussi1
Organizations: 1Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, SF 90014 Oulun yliopisto, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
Language: English
Published: Duke University Press, 2017
Publish Date: 2019-06-04
Description:

# Abstract

We continue the study begun by the third author of $$C^*$$-Segal algebra valued function algebras, with an emphasis on the order structure. Our main result is a characterization theorem for $$C^*$$-Segal algebra valued function algebras with an order unitization. As an intermediate step, we establish a function algebraic description of the multiplier module of arbitrary Segal algebra valued function algebras. We also consider Gelfand representation of these algebras in the commutative case.

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Series: Banach journal of mathematical analysis
ISSN: 1735-8787
ISSN-E: 1735-8787
ISSN-L: 1735-8787
Volume: 11
Issue: 1
Pages: 207 - 222
DOI: 10.1215/17358787-3784682