Positive Derivations on Partially Ordered Linear Algebra With an Order Unit

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Oct 1978Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 72, page 21 (issn: 0002-9939,

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Authors: Dai, Taen-Yu; DeMarr, Ralph;

doi: 10.2307/2042525 , 10.1090/s0002-9939-1978-0491402-4

Positive Derivations on Partially Ordered Linear Algebra With an Order Unit

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Abstract

We show that the range of a positive derivation on a Dedekind σ \sigma -complete partially ordered linear algebra with an order unit is a set of generalized nilpotents. With additional assumptions on the algebra, we show that the algebra has an important property similar to a property of the algebra of upper triangular matrices.

Keywords

Banach lattices, Ordered rings, algebras, modules, Order Unit, Partially Ordered Linear Algebra, Miscellaneous inequalities involving matrices, Generalized Nilpotents, Algebra of Upper Triangular Matrices, Dedekind Sigma-Complete, Linear operators on ordered spaces, Positive Derivations, Ordered topological linear spaces, vector lattices

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