Is there a standard notation for the operator which returns the conic hull w.r.t to the first orthant of a set, i.e. the operator
$V\mapsto\{x\in \mathbb{R}^s_+ : x=y-z,\ y\in\operatorname{co}(V),\ z\in\mathbb{R}^s_+\}$,
where $\operatorname{co} V=\{x\in \mathbb{R}^s: x=\sum_{v\in V} t_v v \quad\text{with}\quad \sum_{v\in V}t_v\leq 1,\ t_v>0\}$.