## Abstract

Let {norm of matrix} ṡ {norm of matrix} be a norm on R^{n}. Averaging {norm of matrix} (ε_{1} x_{1}, ..., ε_{n} x_{n}) {norm of matrix} over all the 2^{n} choices of over(ε, →) = (ε_{1}, ..., ε_{n}) ∈ {- 1, + 1}^{n}, we obtain an expression | | | x | | | which is an unconditional norm on R^{n}. Bourgain, Lindenstrauss and Milman [J. Bourgain, J. Lindenstrauss, V.D. Milman, Minkowski sums and symmetrizations, in: Geometric Aspects of Functional Analysis (1986/1987), Lecture Notes in Math., vol. 1317, Springer, Berlin, 1988, pp. 44-66] showed that, for a certain (large) constant η > 1, one may average over ηn (random) choices of over(ε, →) and obtain a norm that is isomorphic to | | | ṡ | | |. We show that this is the case for any η > 1.

Original language | English |
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Pages (from-to) | 492-497 |

Number of pages | 6 |

Journal | Journal of Functional Analysis |

Volume | 251 |

Issue number | 2 |

DOIs | |

State | Published - 15 Oct 2007 |

## Keywords

- Bourgan-Lindenstrauss-Milman inequality
- Kahane-Khinchin averages
- Unconditional