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Interpolation of Ideal Measures by Abstract K and J Spaces

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Abstract

We work with the abstract K and J interpolation method generated by a sequence lattice Γ. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Γ.

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Authors and Affiliations

  1. Sección Departamental de Matemática Aplicada, Escuela de Estadística, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Luz M. Fernández-Cabrera

  2. Departamento de Matemática Aplicada I, E.T.S. Ingenieros Industriales, Universidad de Vigo, 36200, Vigo, Spain

    Antón Martínez

Authors
  1. Luz M. Fernández-Cabrera
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  2. Antón Martínez
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Correspondence to Luz M. Fernández-Cabrera.

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The authors have been supported in part by the Spanish Ministerio de Educación y Ciencia (MTM2004-01888)

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Fernández-Cabrera, L.M., Martínez, A. Interpolation of Ideal Measures by Abstract K and J Spaces. Acta Math Sinica 23, 1357–1374 (2007). https://doi.org/10.1007/s10114-007-0948-2

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  • DOI: https://doi.org/10.1007/s10114-007-0948-2

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