### Abstract

Under rather general conditions on the matrix entries, we obtain estimates for the probability distribution of the norm of a random matrix transformation from l^{2} to l^{q} (2 ≦ q <∞). Asymptotically, the expected norm is remarkably small and this enables us to produce an interesting class of bounded linear operators from l^{2} to l^{q}. As an application, we complete the characterization of (p, q)- absolutely summing operators on Hilbert space, thereby answering a question left open by several previous authors.

Original language | English (US) |
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Pages (from-to) | 359-365 |

Number of pages | 7 |

Journal | Pacific Journal of Mathematics |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1975 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Bennett, G., Goodman, V., & Newman, C. M. (1975). Norms of random matrices.

*Pacific Journal of Mathematics*,*59*(2), 359-365. https://doi.org/10.2140/pjm.1975.59.359