Blower, Gordon and Ransford, T. J. (2004) *Complex uniformly convex Banach spaces and Riesz measures.* Canadian Journal of Mathematics, 56 (2). pp. 225-245. ISSN 0008-414X

## Abstract

The norm on a Banach space gives rise to a subharmonic function on the complex plane for which the distributional Laplacian gives a Riesz measure. This measure is calculated explicitly here for Lebesgue Lp spaces and the von~Neumann-Schatten trace ideals. Banach spaces that are q-uniformly PL-convex in the sense of Davis, Garling and Tomczak-Jaegermann are characterized in terms of the mass distribution of this measure. This gives a new proof that the trace ideals cp are 2-uniformly PL-convex for 1 leq p leq 2.

Item Type: | Article |
---|---|

Journal or Publication Title: | Canadian Journal of Mathematics |

Additional Information: | RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics |

Uncontrolled Keywords: | subharmonic functions ; Banach spaces ; Schatten trace ideals |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 2368 |

Deposited By: | ep_importer |

Deposited On: | 01 Apr 2008 15:20 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 07 Jan 2015 13:48 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2368 |

### Actions (login required)

View Item |