bilattice

English

Etymology

bi- +‎ lattice

Noun

bilattice (plural bilattices)

1. (mathematics, computing) A structure B = (S,⊑₁ ,⊑₂) in which S is a non-empty set, and ⊑₁ and ⊑₂ are partial orderings each giving S the structure of a lattice, determining thus for each of the two lattices the corresponding operations of meet and join.
   • 2015, Janko Bračič, Lina Oliveira, “A characterization of reflexive spaces of operators”, in arXiv‎^[1]:

     We show that for a linear space of operators ${\mathcal {M}}\subseteq {\mathcal {B}}(H_{1},H_{2})$ the following assertions are equivalent. (i) ${\mathcal {M}}$ is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map $1$ on a bilattice $Bil({\mathcal {M}})$ of subspaces determined by ${\mathcal {M}}$, with $P\leq \psi _{1}(P,Q)$ and $Q\leq \psi _{2}(P,Q)$, for any pair $(P,Q)\in Bil({\mathcal {M}})$, and such that an operator $T\in {\mathcal {B}}(H_{1},H_{2})$ lies in ${\mathcal {M}}$ if and only if $\psi _{2}(P,Q)T\psi _{1}(P,Q)=0$ for all $(P,Q)\in Bil({\mathcal {M}})$.