Jameson, Graham J. O. (1996) *2-convexity and 2-concavity in Schatten ideals.* Mathematical Proceedings of the Cambridge Philosophical Society, 120 (4). pp. 697-701. ISSN 0305-0041

## Abstract

The properties p-convexity and q-concavity are fundamental in the study of Banach sequence spaces (see [L-TzII]), and in recent years have been shown to be of great significance in the theory of the corresponding Schatten ideals ([G-TJ], [LP-P] and many other papers). In particular, the notions 2-convex and 2-concave are meaningful in Schatten ideals. It seems to have been noted only recently [LP-P] that a Schatten ideal has either of these properties if the underlying sequence space has. One way of establishing this is to use the fact that if (E, E) is 2-convex, then there is another Banach sequence space (F, F) such that x; = x2F for all x ε E. The 2-concave case can then be deduced using duality, though this raises some difficulties, for example when E is inseparable.

Item Type: | Article |

Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society |

Additional Information: | http://journals.cambridge.org/action/displayJournal?jid=PSP The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 120 (4), pp 697-701 1996, © 1996 Cambridge University Press. |

Subjects: | Q Science > QA Mathematics |

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

ID Code: | 19534 |

Deposited By: | ep_ss_importer |

Deposited On: | 11 Nov 2008 15:17 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 05 Sep 2016 00:01 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19534 |
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