A duality theorem for interpolation methods associated to polygons

Cobos, Fernando; Fernández-Martínez, Pedro

doi:10.1090/S0002-9939-1994-1209420-6

A duality theorem for interpolation methods associated to polygons
HTML articles powered by AMS MathViewer

by Fernando Cobos and Pedro Fernández-Martínez

Proc. Amer. Math. Soc. 121 (1994), 1093-1101

DOI: https://doi.org/10.1090/S0002-9939-1994-1209420-6

PDF | Request permission

Abstract:

We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified with closed subspaces of K-spaces generated by the dual N-tuple.

References

Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275
Fernando Cobos and Pedro Fernández-Martínez, Reiteration and a Wolff theorem for interpolation methods defined by means of polygons, Studia Math. 102 (1992), no. 3, 239–256. MR 1170554, DOI 10.4064/sm-102-3-239-256
Fernando Cobos, Pedro Fernández-Martínez, and Tomas Schonbek, Norm estimates for interpolation methods defined by means of polygons, J. Approx. Theory 80 (1995), no. 3, 321–351. MR 1320157, DOI 10.1006/jath.1995.1021
Fernando Cobos, Thomas Kühn, and Tomas Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Anal. 106 (1992), no. 2, 274–313. MR 1165856, DOI 10.1016/0022-1236(92)90049-O
Fernando Cobos and Jaak Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. (3) 63 (1991), no. 2, 371–400. MR 1114514, DOI 10.1112/plms/s3-63.2.371
R. R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher, and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. in Math. 43 (1982), no. 3, 203–229. MR 648799, DOI 10.1016/0001-8708(82)90034-2
John B. Conway, A course in functional analysis, Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1985. MR 768926, DOI 10.1007/978-1-4757-3828-5
Michael Cwikel and Svante Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. in Math. 66 (1987), no. 3, 234–290. MR 915856, DOI 10.1016/0001-8708(87)90036-3
Giovanni Dore, Davide Guidetti, and Alberto Venni, Some properties of the sum and the intersection of normed spaces, Atti Sem. Mat. Fis. Univ. Modena 31 (1982), no. 2, 325–331 (1984) (English, with Italian summary). MR 742678
Giovanni Dore, Davide Guidetti, and Alberto Venni, Complex interpolation for $2^N$ Banach spaces, Rend. Sem. Mat. Univ. Padova 76 (1986), 1–36 (English, with Italian summary). MR 881557
Dicesar Lass Fernandez, Interpolation of $2^{n}$ Banach spaces, Studia Math. 65 (1979), no. 2, 175–201. MR 557490, DOI 10.4064/sm-65-2-175-201
Dicesar Lass Fernandez, On the duality of interpolation spaces of several Banach spaces, Acta Sci. Math. (Szeged) 44 (1982), no. 1-2, 43–51. MR 660511
Dicesar Lass Fernandez, Interpolation of $2^d$ Banach spaces and the Calderón spaces $X(E)$, Proc. London Math. Soc. (3) 56 (1988), no. 1, 143–162. MR 915534, DOI 10.1112/plms/s3-56.1.143
Jaak Peetre, Duality for Fernandez type spaces, Math. Nachr. 119 (1984), 231–238. MR 774193, DOI 10.1002/mana.19841190122
Gunnar Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. (4) 99 (1974), 247–316. MR 372641, DOI 10.1007/BF02413728