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On interpolation of bilinear operators by methods associated to polygons


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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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

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