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Interpolation of compactness using Aronszajn-Gagliardo functors

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Abstract

We prove that ifT: A 0 →B 0 andT: A 1 →B 1 both are compact, then\(T:F(\bar A) \to F(\bar B)\) is also compact, whereF is the minimal or the maximal functor in the sense of Aronszajn-Gagliardo. We also derive some results for ordered couples.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Fernando Cobos

  2. Matematiska Institutionen, Box 6701, S-11385, Stockholm, Sweden

    Jaak Peetre

Authors
  1. Fernando Cobos
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  2. Jaak Peetre
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Supported in part by Ministerio de Educación y Ciencia (SAB-87-0172).

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Cobos, F., Peetre, J. Interpolation of compactness using Aronszajn-Gagliardo functors. Israel J. Math. 68, 220–240 (1989). https://doi.org/10.1007/BF02772662

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  • DOI: https://doi.org/10.1007/BF02772662

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