Cobos, Fernando and Cordeiro, José María and Martínez, Antón
(1999)
*On interpolation of bilinear operators by methods associated to polygons.*
Bollettino della Unione Matematica Italiana, 8
(2B).
pp. 319-330.
ISSN 0041-7084
(In Press)

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## Abstract

The authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [Proc. Lond. Math. Soc., III. Ser. 63, 371-400 (1991; Zbl 0727.46053)]. The main properties of methods defined by polygons are summarized and then a bilinear interpolation theorem for a combination of the K- and J-methods is established. Another bilinear interpolation theorem for the J-method is given and a counterexample shows that a similar result fails for the K-method.

The final part contains an application to interpolation of operator spaces starting from Banach lattices.

Item Type: | Article |
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Uncontrolled Keywords: | Behaviour of bilinear operators under interpolation; methods defined by polygons; combination of the K- and J-methods |

Subjects: | Sciences > Mathematics > Numerical analysis |

ID Code: | 15465 |

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Deposited On: | 01 Jun 2012 10:54 |

Last Modified: | 25 Oct 2013 13:12 |

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