Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2003-03-31
On Positive-off-Diagonal Operators on Ordered Normed SpacesAnke Kalauch (1) Technische Universität Dresden, Germany
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.
Keywords: Positive-off-diaganol operators, ordered normed spaces, Riesz decomposition property
Kalauch Anke: On Positive-off-Diagonal Operators on Ordered Normed Spaces. Z. Anal. Anwend. 22 (2003), 229-238. doi: 10.4171/ZAA/1142