Cobos Díaz, 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)
![[img]](/style/images/fileicons/application_pdf.png) | PDF Restricted to Repository staff only 225Kb |
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 |
| References: | 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 Function Theory, 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. |
| Deposited On: | 01 Jun 2012 12:54 |
| Last Modified: | 01 Jun 2012 12:54 |
Repository Staff Only: item control page
