A CHARACTERISATION OF CENTRAL ELEMENTS IN $C^{\ast }$-ALGEBRAS. Issue 1 (19th October 2016)

• Record Type: Journal Article
• Authors: MOLNÁR, LAJOS
• Is Part Of: Bulletin of the Australian Mathematical Society. Volume 95:Issue 1(2017)
• Page Start: 138
• Page End: 143
• Publication Date: 2016-10-19
• Subjects: primary 46L05, -- secondary 47B49; C∗ -algebra, -- central element, -- order, -- exponential function; Mathematics -- Societies, etc; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S000497271600068X
• Languages: English
• ISSNs: 0004-9727

Abstract

Abstract : Wu ['An order characterization of commutativity for $C^{\ast }$ -algebras', Proc. Amer. Math. Soc. 129 (2001), 983–987] proved that if the exponential function on the set of all positive elements of a $C^{\ast }$ -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 $C^{\ast }$ -algebras in terms of the order.