Definition:Cone (Vector Space)

Definition

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

Let $X$ be a vector space over $\GF$.

Let $P \subseteq X$.

We say that $P$ is a cone if and only if:

for all $\alpha \in \R_{\ge 0}$ and $v \in P$, we have $\alpha v \in P$.

Sources

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