Pestman, Wiebe R. A quick and simple proof of Sherman’s theorem on order in \(C^*\)-algebras. (English) Zbl 0899.46039 Bull. Belg. Math. Soc. - Simon Stevin 3, No. 4, 407-409 (1996). The title of this short note says it all. S. Sherman [Am. J. Math. 73, 227-232 (1951; Zbl 0042.35001)] proved that if the positive cone in a \(C^*\)-algebra is a lattice, then the algebra is commutative. Reviewer: Kh.N.Boyadzhiev (Ada) MSC: 46L05 General theory of \(C^*\)-algebras 46A40 Ordered topological linear spaces, vector lattices Citations:Zbl 0042.35001 PDFBibTeX XMLCite \textit{W. R. Pestman}, Bull. Belg. Math. Soc. - Simon Stevin 3, No. 4, 407--409 (1996; Zbl 0899.46039) Full Text: EuDML