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.
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