Definition:Preordering Induced by Convex Cone
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Definition
Let $\GF \in \set {\R, \C}$.
Let $X$ be a vector space over $\GF$.
Let $P \subseteq X$ be a convex cone in $X$.
Define a relation $\succeq^P$ by:
- $v \succeq^P v'$ if and only if $v - v' \in P$
for each $v, v' \in X$.
We say that $\succeq^P$ is the preordering on $X$ induced by $P$.
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