Isotone Functions on Partially Ordered Linear Algebras with a Multiplicative Diagonal Map

Abstract

The diagonal of the product of two triangular matrices is the product of the diagonals of each matrix. This idea is used to characterize Dedekind o-complete lattice ordered linear algebras which admit isotone functions with familiar functional and order properties as possessed by the real-valued logarithm or root function.

Elementary Functional Equations on Partially Ordered Linear Algebra

“…Introduction and definitions. This note is motivated by the work in [6] and the study of Cauchy functional equations [1, pp. 37-40], namely, functions having one of the following properties:…”