Integral Equations and Operator Theory

, Volume 66, Issue 1, pp 79–112 | Cite as

Interpolation of Banach Lattices and Factorization of p-Convex and q-Concave Operators



We extend a result of Šestakov to compare the complex interpolation method [X 0, X 1]θ with Calderón-Lozanovskii’s construction \({{{{X^{1-\theta}_{0}X^{\theta}_{1}}}}}\), in the context of abstract Banach lattices. This allows us to prove that an operator between Banach lattices T : EF which is p-convex and q-concave, factors, for any \({{{{\theta \in (0, 1)}}}}\), as TT 2 T 1, where T 2 is (\({{\left({\frac{p}{{\theta + (1 - \theta)p}}} \right)}}\)-convex and T 1 is \({{\left({\frac{q}{{1 - \theta }}} \right)}}\)-concave.

Mathematics Subject Classification (2010)

Primary 47B60 Secondary 46B42 46B70 


Interpolation of Banach lattices method of Calderón-Lozanovskii factorization p-convex operator q-concave operator 


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© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu, CNRS and UPMC-Univ. Paris-06ParisFrance
  2. 2.Departamento de Análisis MatemáticoUniversidad Complutense de MadridMadridSpain

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