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

Arhippainen, Jorma; Kauppi, Jukka; Mattas, Jussi (2016-12-09)
 
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https://doi.org/10.1215/17358787-3784682

Arhippainen, Jorma
Kauppi, Jukka
Mattas, Jussi
Duke University Press
09.12.2016

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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© 2017 Tusi Mathematical Research Group and Duke University Press. The final publication is available at https://projecteuclid.org/euclid.bjma/1481274115
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doi:https://doi.org/10.1215/17358787-3784682
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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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