**2-convexity and 2-concavity in Schatten ideals.**252 KB, PDF-document

Date added: 3/11/15

Research output: Contribution to journal › Journal article

Published

<mark>Journal publication date</mark> | 11/1996 |
---|---|

<mark>Journal</mark> | Mathematical Proceedings of the Cambridge Philosophical Society |

Issue number | 4 |

Volume | 120 |

Number of pages | 5 |

Pages (from-to) | 697-701 |

<mark>State</mark> | Published |

<mark>Original language</mark> | English |

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.

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.