A CHARACTERISATION OF CENTRAL ELEMENTS IN $C^{* }$-ALGEBRAS. Issue 1 (19th October 2016) - MOLNÁR, LAJOS
Abstract : Wu ['An order characterization of commutativity for $C^{* }$ -algebras', Proc. Amer. Math. Soc. 129 (2001), 983–987] proved that if the exponential function on the set of all positive elements of a $C^{* }$ -algebra is monotone in the usual partial order, then the algebra in question is necessarily commutative. In this note, we present a local version of that result and obtain a characterisation of central elements in $C^{* }$ -algebras in terms of the order.