### Abstract

We present a new and constructive proof of the Peter-Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*-algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2].

Original language | English |
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Pages (from-to) | 351-359 |

Journal | Mathematical Logic Quarterly |

Volume | 51 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2005 |

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## Cite this

Coquand, T., & Spitters, B. A. W. (2005). A constructive proof of the Peter-Weyl theorem.

*Mathematical Logic Quarterly*,*51*(4), 351-359. https://doi.org/10.1002/malq.200410037