×

A quick and simple proof of Sherman’s theorem on order in \(C^*\)-algebras. (English) Zbl 0899.46039

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.

MSC:

46L05 General theory of \(C^*\)-algebras
46A40 Ordered topological linear spaces, vector lattices

Citations:

Zbl 0042.35001
PDFBibTeX XMLCite
Full Text: EuDML