JournalszaaVol. 22 , No. 1DOI 10.4171/zaa/1142

On Positive-off-Diagonal Operators on Ordered Normed Spaces

  • Anke Kalauch

    Technische Universität Dresden, Germany
On Positive-off-Diagonal Operators on Ordered Normed Spaces cover

Abstract

On a normed space X ordered by a cone K we consider a continuous linear operator A from X to X of the following kind: If a positive continuous functional f attains 0 on some positive element x, then f(Ax) is greater or equal to 0. If X is a vector lattice, then such operators can be represented as sI + B, where B is a positive operator, I is the identity and s is a real number. We generalize this assertion for weaker assumptions on X, using the Riesz decomposition property.