See bilattice on Wiktionary
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"ref": "2015, Janko Bračič, Lina Oliveira, “A characterization of reflexive spaces of operators”, in arXiv:",
"text": "We show that for a linear space of operators #x7B;#x5C;mathcalM#x7D;#x5C;subseteq#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) the following assertions are equivalent. (i) #x7B;#x5C;mathcalM#x7D; is reflexive in the sense of Loginov--Shulman. (ii) There exists an order-preserving map 1 on a bilattice Bil(#x7B;#x5C;mathcalM#x7D;) of subspaces determined by #x7B;#x5C;mathcalM#x7D;, with P#x5C;leq#x5C;psi#x5F;1(P,Q) and Q#x5C;leq#x5C;psi#x5F;2(P,Q), for any pair (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;), and such that an operator T#x5C;in#x7B;#x5C;mathcalB#x7D;(H#x5F;1,H#x5F;2) lies in #x7B;#x5C;mathcalM#x7D; if and only if #x5C;psi#x5F;2(P,Q)T#x5C;psi#x5F;1(P,Q)#x3D;0 for all (P,Q)#x5C;inBil(#x7B;#x5C;mathcalM#x7D;).",
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"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."
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"(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."
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Download raw JSONL data for bilattice meaning in All languages combined (2.2kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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