Sentence examples similar to be an bilinear functional from inspiring English sources

Let be a bilinear functional.

Let be a bilinear functional such that separates points in.

Let be a bilinear functional which is continuous over compact subsets of.

Let and be vector spaces over, let be a bilinear functional, and let be a nonempty subset of.

Let be a topological vector space over, let be a vector space over and let be a bilinear functional.

Definition 1.1.. Let and be a vector spaces over, let be a bilinear functional, and let be a nonempty subset of.

Let be a bilinear functional such that separates points in, is continuous over compact subsets of, and, for any, the mapping is continuous on.

Let E be a topological vector space over Φ, F be a vector space over Φ and X be a nonempty subset of E. Let 〈 ⋅, ⋅ 〉 : F × E → Φ be a bilinear functional.

Let E be a topological vector space over Φ, F be a vector space over Φ and X be a non-empty subset of E. Let 〈·, ·〉 F × E → Φ be a bilinear functional.

Lemma 2.3 Let E be a Hausdorff topological vector space over Φ, A ∈ F ( E ) and X = co ( A ), where co ( A ) denotes the convex hull of A. Let F be a vector space over Φ and 〈 ⋅, ⋅ 〉 : F × E → ϕ be a bilinear functional such that 〈 ⋅, ⋅ 〉 separates points in F. We equip F with the σ 〈 F, E 〉 -topology.

Let E be a locally convex Hausdorff topological vector space over Φ, X be a non-empty compact convex subset of E and F be a vector space over Φ with σ〈F, E〉-topology where 〈·, ·〉 : F × E → Φ is a bilinear functional such that for each w ∈ F, the function x ↦ Re 〈w, x〉 is continuous.