### Abstract

Let (M) be the bounded continuous functions on a topological space M. "Almost linear" operators (and functionals) on C(M) are defined. Almost linearity does not imply linearity in general. However, it is shown that if M = [O, l] then any almost linear operator (or functional) must be linear. Specifically, if (a)0 implies T(f) 0, (b) T(f + g) = T(f) + T(g) whenever fg = 0, (c) T(f + g) = T(f) + T(g) whenever g is constant, and M[O, l], then T is linear. An application is given to convergence of measur.

Original language | English (US) |
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Pages (from-to) | 147-154 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1975 |

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## Cite this

Baxter, J. R., & Chacon, R. V. (1975). Almost linear operators and functionals.

*Proceedings of the American Mathematical Society*,*47*(1), 147-154. https://doi.org/10.1090/S0002-9939-1975-0352380-9