### Abstract

Wu ['An order characterization of commutativity for -algebras', Proc. Amer. Math. Soc. 129 (2001), 983-987] proved that if the exponential function on the set of all positive elements of a -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 -algebras in terms of the order.

Original language | English |
---|---|

Pages (from-to) | 138-143 |

Number of pages | 6 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 95 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2017 |

### Fingerprint

### Keywords

- central element
- C∗-algebra
- exponential function
- order

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**A characterisation of central elements in C∗-algebras.** / Molnár, L.

Research output: Contribution to journal › Article

*Bulletin of the Australian Mathematical Society*, vol. 95, no. 1, pp. 138-143. https://doi.org/10.1017/S000497271600068X

}

TY - JOUR

T1 - A characterisation of central elements in C∗-algebras

AU - Molnár, L.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Wu ['An order characterization of commutativity for -algebras', Proc. Amer. Math. Soc. 129 (2001), 983-987] proved that if the exponential function on the set of all positive elements of a -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 -algebras in terms of the order.

AB - Wu ['An order characterization of commutativity for -algebras', Proc. Amer. Math. Soc. 129 (2001), 983-987] proved that if the exponential function on the set of all positive elements of a -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 -algebras in terms of the order.

KW - central element

KW - C∗-algebra

KW - exponential function

KW - order

UR - http://www.scopus.com/inward/record.url?scp=84991730408&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84991730408&partnerID=8YFLogxK

U2 - 10.1017/S000497271600068X

DO - 10.1017/S000497271600068X

M3 - Article

VL - 95

SP - 138

EP - 143

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 1

ER -