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  • Cited by 9
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Brudnyi, Yu. 2015. Interpolation of compact operators by general interpolation methods. Journal of Functional Analysis, Vol. 268, Issue. 6, p. 1382.

    Cobos, Fernando Fernández-Cabrera, Luz M. and Martínez, Antón 2015. On a paper of Edmunds and Opic on limiting interpolation of compact operators between Lp spaces. Mathematische Nachrichten, Vol. 288, Issue. 2-3, p. 167.

    Cobos, Fernando and Kühn, Thomas 2014. Extrapolation results of Lions-Peetre type. Calculus of Variations and Partial Differential Equations, Vol. 49, Issue. 1-2, p. 847.

    FAN, MING 2013. K-ENVELOPES FOR REAL INTERPOLATION METHODS. Glasgow Mathematical Journal, Vol. 55, Issue. 02, p. 293.

    Mastyło, Mieczysław 2010. Interpolation estimates for entropy numbers with applications to non-convex bodies. Journal of Approximation Theory, Vol. 162, Issue. 1, p. 10.

    Cobos, Fernando Fernández–Cabrera, Luz M. and Martínez, Antón 2007. AbstractK andJ spaces and measure of non-compactness. Mathematische Nachrichten, Vol. 280, Issue. 15, p. 1698.

    Fernández-Cabrera, Luz M. and Martínez, Antón 2007. Interpolation of Ideal Measures by Abstract K and J Spaces. Acta Mathematica Sinica, English Series, Vol. 23, Issue. 8, p. 1357.

    Cobos, Fernando Fernández-Cabrera, Luz M. Manzano, Antonio and Martínez, Antón 2005. On interpolation of Asplund operators. Mathematische Zeitschrift, Vol. 250, Issue. 2, p. 267.

    Cobos, Fernando Fernández-Cabrera, Luz M. Manzano, Antonio and Martı́nez, Antón 2004. Real interpolation and closed operator ideals☆☆Authors have been supported in part by Ministerio de Ciencia y Tecnologı́a (BFM2001-1424).. Journal de Mathématiques Pures et Appliquées, Vol. 83, Issue. 3, p. 417.

  • Proceedings of the Edinburgh Mathematical Society, Volume 44, Issue 1
  • February 2001, pp. 153-173


  • Fernando Cobos (a1), Michael Cwikel (a2) and Pedro Matos (a1) (a3)
  • DOI:
  • Published online: 20 January 2009

If $T:A_{0}\rightarrow B$ boundedly and $T:A_{1}\rightarrow B$ compactly, then a result of Lions–Peetre shows that $T:A\rightarrow B$ compactly for a certain class of spaces $A$ which are intermediate with respect to $A_{0}$ and $A_{1}$. We investigate to what extent such results can hold for arbitrary intermediate spaces $A$. The ‘dual’ case of an operator $S$ such that $S:X\rightarrow Y_{0}$ boundedly and $S:X\rightarrow Y_{1}$ compactly, is also considered, as well as similar questions for other closed operator ideals.

AMS 2000 Mathematics subject classification: Primary 46B70; 47D50

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
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