## Abstract

Let I⊂ ℝ be open, let k∈ N_{0} and T : C^{k}(I) →C^{k}(I) be bijective, pointwise continuous and submultiplicative, i.e., (Formula presented) Suppose also that T (-1) < 0 and that T and T^{-1} are positivity preserving. We show that there is a homeomorphism u : I → I and that there are continuous functions p,A ∈ C(I) with p > 0, A ≥ 1 such that (Formula presented). For k ∈ N, we have A = p = 1, and u is a C^{k}-diffeomorphismus so that Tf(u(x)) = f(x), i.e., T is multiplicative for k ∈ N. This rigidity property also holds for supermultiplicative operators.

Original language | English |
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Title of host publication | Operator Theory |

Subtitle of host publication | Advances and Applications |

Publisher | Springer International Publishing |

Pages | 267-279 |

Number of pages | 13 |

DOIs | |

State | Published - 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
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Volume | 261 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

## Keywords

- Approximate indicator
- Positivity preserving diffeomorphism
- Submultiplicative operators

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