## Abstract

For a compact space X, any group automorphism ψ of C(X,double struk D sign^{1}) induces a mapping Θ on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Θ equivalent to θ_{ψ}, is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when ψ(-1) = -1. Indeed, Θ is a Boolean isomorphism iff θ_{ψ} preserves the product of projections. If X is equipped with a probability measure μ, on a certain σ-algebra of X, we show (under some condition) that Θ preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping θ_{ψ} is μ-orthoisomorphism on the projections of the C*-algebra C(X).

Original language | English |
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Pages (from-to) | 439-451 |

Number of pages | 13 |

Journal | Turkish Journal of Mathematics |

Volume | 31 |

Issue number | 4 |

Publication status | Published - Dec 1 2007 |

Externally published | Yes |

## Keywords

- Almost isomorphisms
- Boolean algebra
- Clopen subset
- Projections
- Unitary

## ASJC Scopus subject areas

- Mathematics(all)