We show that every continuous self-adjoint functional on the noncommutative Schwartz space can be decomposed into a difference of two positive functionals. Moreover, this decomposition is minimal in the natural sense.

We verify our earlier conjecture and use it to prove that the semisimple parts of the rational Jordan–Kac–Vinberg decompositions of a rational vector all lie in a single rational orbit.

This paper develops a general technique for the computation of comparative dynamics in perfect-foresight discrete-time models. The method developed here is both applicable and general; it can be used to analyze the effects of the perturbation of parameters on endogenous variables and the welfare of an economic system derived from more general multisector models. It is neither restricted to the system's dimensions nor restricted by the assumption of distinct eigenvalues in the system.

We study conditions under which every delta-convex (d.c.) mapping is the difference of two continuous convex operators, and vice versa. In particular, we prove that each d.c. mapping $F:(a,b)\to Y$ is the difference of two continuous convex operators whenever $Y$ belongs to a large class of Banach lattices which includes all $L^{p}(\mu)$ spaces ($1\leq p\leq\infty$). The proof is based on a result about Jordan decomposition of vector-valued functions. New observations on Jordan decomposition of finitely additive vector-valued measures are also presented.