Positivity

, Volume 15, Issue 2, pp 241–251 | Cite as

c0-Singular and 1-singular operators between vector-valued Banach lattices

Article

Abstract

Given an operator T : XY between Banach spaces, and a Banach lattice E consisting of measurable functions, we consider the point-wise extension of the operator to the vector-valued Banach lattices TE : E(X) → E(Y) given by TE(f)(ω) = T(f(ω)). It is proved that for any Banach lattice E which does not contain c0, the operator T is an isomorphism on a subspace isomorphic to c0 if and only if so is TE. An analogous result for invertible operators on subspaces isomorphic to 1 is also given.

Keywords

Vector-valued Banach lattice c0-Singular operator 1-Singular operator 

Mathematics Subject Classification (2000)

47A05 46B42 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada y AnálisisUniversidad de BarcelonaBarcelonaSpain

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