Proceedings of the 3rd International Conference on Topological Algebra and Applications, Oulu 2–6 July, 2001

Abstract The 3rd International Conference on Topological Algebra and Applications (ICTAA 3) was held at the University of Oulu in July 02-06, 2001. The conference had over 40 participants with more than 30 contributed talks. These proceedings consist of 19 articles written based on the talks presented at the conference. We wish to thank the following sponsors for their generous financial support: Rolf Nevanlinna Institute, Finnish Mathematical Society, Vilho, Yrj? and Kalle V?is?l? foundation and the Department of Mathematical Sciences in Oulu

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 Gelfand representation of these algebras in the commutative case