### Abstract

Let ℸ^{+} be the positive cone in a totally ordered abelian group ℸ. We construct crossed products by actions of ℸ^{+} as endomorphisms of Calgebras, and give criteria which ensure a given representation of the crossed product is faithful. We use this to prove that the C* -algebras generated by two semigroups V, W: ℸ^{+} → B (H) of nonunitary isometries are canonically isomorphic, thus giving a new, self-contained proof of a theorem of Murphy, which includes earlier results of Coburn and Douglas.

Original language | English (US) |
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Pages (from-to) | 1133-1141 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 122 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1994 |

### Keywords

- C*-algebra
- Covariant representation
- Crossed product
- Endomorphism
- Ordered group
- Semigroup of isometries
- Toeplitz algebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Adji, S., Laca, M., Nilsen, M., & Raeburn, I. (1994). Crossed products by semigroups of endomorphisms and the toeplitz algebras of ordered groups.

*Proceedings of the American Mathematical Society*,*122*(4), 1133-1141. https://doi.org/10.1090/S0002-9939-1994-1215024-1