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On interpolation of bilinear operators by methods associated to polygons

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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
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
Deposited On:01 Jun 2012 10:54
Last Modified:25 Oct 2013 13:12

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