## Banach Journal of Mathematical Analysis

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

#### 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 the Gelfand representation of these algebras in the commutative case.

#### Article information

Source
Banach J. Math. Anal., Volume 11, Number 1 (2017), 207-222.

Dates
Received: 2 November 2015
Accepted: 17 March 2016
First available in Project Euclid: 9 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1481274115

Digital Object Identifier
doi:10.1215/17358787-3784682

Mathematical Reviews number (MathSciNet)
MR3582396

Zentralblatt MATH identifier
1362.46051

#### Citation

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

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