RT Journal Article T1 On interpolation of bilinear operators by methods associated to polygons A1 Cobos, Fernando A1 Cordeiro, José María A1 Martínez, Antón AB 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. PB Unione matematica italiana SN 0041-7084 YR 1999 FD 1999 LK https://hdl.handle.net/20.500.14352/57312 UL https://hdl.handle.net/20.500.14352/57312 LA eng NO S. V. ASTASHKIN, On interpolation of bilinear operators with a real method, Mat. Zametki, 52 (1992), 15-24. J. BERGH - J. LÖFSTRÖM, «Interpolation Spaces. An Introduction», Springer, Berlin-Heidelberg-New York (1976). F. COBOS - P. FERNÁNDEZ-MARTÍNEZ, A duality theorem for interpolation methods associated to polygons, Proc. Amer. Math. Soc. 121, (1994), 1093-1101. F. COBOS - P. FERNÁNDEZ-MARTÍNEZ - A. MARTÍNEZ, On reiteration and the behavior of weak compactness under certain interpolation methods, Collect. Math. (to appear). F. COBOS - P. FERNÁNDEZ-MARTÍNEZ, A. MARTÍNEZ - Y. RAYNAUD, On duality between K- and J-spaces, Proc. Edinburgh Math. Soc. (to appear). F. COBOS - P. FERNÁNDEZ-MARTÍNEZ - T. SCHONBEK, Norm estimates for interpolation methods defined by means of polygons, J. Approx. Theory, 80 (1995), 321-351. F. COBOS - J. PEETRE, Interpolation of compact operators: The multidimensional case, Proc. London Math. Soc., 63 (1991), 371-400. M. CWIKEL - S. JANSON, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. Math., 66 (1987), 234-290. A. FAVINI, Some results on interpolation of bilinear operators, Boll. Un. Mat. Ital., 15 (1978), 170-181. D. L. FERNÁNDEZ, Interpolation of 2d Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc., 56 (1988), 143-162. S. JANSON, On interpolation of multi-linear operators, in Function Spaces and Applications, Proceedings, Lund 1986, Lect. Notes Math., 1302 (1988), 290-302. J. L. LIONS - J. PEETRE, Sur une classe d’espaces d’interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19 (1964), 5-68. J. PEETRE, Paracommutators and minimal spaces, in Operators and Funtion Theory,Proceedings of the NATO Advanced Study Institute on Operators and FunctionTheory, Lancaster, 1984, ed. S. C. Power, Reidel, Dordrecht (1985), 163-223. G. SPARR, Interpolation of several Banach spaces, Ann. Math. Pura Appl., 99 (1974), 247-316. H. TRIEBEL, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam (1978). M. ZAFRAN, A multilinear interpolation theorem, Studia Math., 62 (1978), 107-124. NO DGICYT DS Docta Complutense RD 5 dic 2023