On reiteration and the behaviour of weak compactness under certain interpolation methods

• Autores: Antonio Martínez Abejón , Pedro Fernández Martínez , Fernando Cobos Díaz
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 50, Fasc. 1, 1999, págs. 53-72
• Idioma: inglés
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• Resumen

  • This article deals with $K$- and $J$-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compactness results.

• Referencias bibliográficas
  • B. Beauzamy, Espaces d’interpolation réels; topologie et géométrie, Lect. Notes in Math. 666, Springer, Berlin, 1978.
  • J. Bergh and J. Löfström, Interpolation spaces. An Introduction, Springer, Berlin-Heidelberg-New York, 1976.
  • M.J. Carro and L.I. Nikolova, Interpolation of limited and weakly compact operators on families of Banach spaces, Acta Appl. Math. 49 (1997),...
  • F. Cobos and P. Fernández Martínez, A duality theorem for interpolation methods associated to polygons, Proc. Amer. Math. Soc. 121 (1994),...
  • F. Cobos, P. Fernández-Martínez and T. Schonbek, Norm estimates for interpolation methods defined by means of polygons, J. Approx. Theory...
  • F. Cobos and J. Peetre, Interpolation of compact operators: The multidimensional case, Proc. London Math. Soc. 63 (1991), 371–400.
  • M. Cwikel and S. Janson, Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. Math. 66 (1987), 234–290.
  • D.L. Fernández, Interpolation of 2nd Banach spaces and the Calderón spaces $X(E)$, Proc. London Math. Soc. 56 (1988), 143–162.
  • S. Heinrich, Closed operator ideals and interpolation, J. Funct. Anal. 35 (1980), 397–411.
  • L. Maligranda and A. Quevedo, Interpolation of weakly compact operators, Arch. Math. 55 (1990), 280–284.
  • M. Mastyło, On interpolation of weakly compact operators, Hokkaido Math. J. 22 (1993), 105–114.
  • G. Sparr, Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247–316.
  • H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam-New York-Oxford, 1978.
  • A. Yoshikawa, Sur la théorie d’espaces d’interpolation: les espaces de moyenne de plusieurs espaces de Banach, J. Fac. Sci. Univ. Tokyo 16...