Definition:Positive Element of Preordered Vector Space

Definition

Let $\GF \in \set {\R, \C}$.

Let $\struct {X, \succeq}$ be a preordered vector space over $\GF$.

Let ${\mathbf 0}_X$ be the zero vector of $X$.

Let $x \in X$.

We say that $x$ is a positive element if and only if $x \succeq {\mathbf 0}_X$.

Sources

• 2023: Jean-Bernard Bru and Walter Alberto de Siqueira Pedra: C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics ... (previous) ... (next): $1.1$: Basic notions