Tsertos, Y. Multiplications and involutions on vector spaces. (English) Zbl 0953.46023 J. Math. Sci., New York 96, No. 6, 3766-3771 (1999). The aim of this paper is to present1) an abstract algebraic form of the classical Vidav-Palmer theorem, pertaining to a characterization of the existence of a \(C^*\)-algebra structure on a given unital Banach algebra and2) an abstract algebraic formulation of the result of Bucy-Maltese, concerning the integral representation of a given positive linear form on a unital commutative Banach \(*\)-algebra. Reviewer: Yuri Movsisyan (Yerevan) Cited in 1 ReviewCited in 1 Document MSC: 46H05 General theory of topological algebras 46K05 General theory of topological algebras with involution 46A55 Convex sets in topological linear spaces; Choquet theory Keywords:Vidav-Palmer theorem; existence of a \(C^*\)-algebra structure; integral representation; positive linear form; unital commutative Banach \(*\)-algebra Citations:Zbl 0930.00011 PDFBibTeX XMLCite \textit{Y. Tsertos}, J. Math. Sci., New York 96, No. 6, 3766--3771 (1999; Zbl 0953.46023) Full Text: DOI References: [1] F. F. Bonsall and J. Duncan,Complete Normed Algebras, Springer-Verlag, Berlin (1973). · Zbl 0271.46039 [2] R. S. Bucy and G. Maltese, ”A representation theorem for positive functionals on involutive algebras,”Math. Ann.,162, 364–367 (1966). · Zbl 0132.10804 · doi:10.1007/BF01369109 [3] A. Mallios,Topological Algebras. Selected Topics, North-Holland, Amsterdam (1986). · Zbl 0597.46046 [4] Y. Tsertos, ”Representations and extensions of positive functionals on *-algebras,”Boll. U. M. I.,8, 541–555 (1994). · Zbl 0834.46038 [5] Y. Tsertos, ”On integral representations of linear forms,”Rend. Circ. Mat. Palermo,46, 309–316 (1997). · Zbl 0893.46045 · doi:10.1007/BF02977031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.