# 關鍵字查詢 | 類別：期刊論文 | | 關鍵字：On the daulity operator of a convex cone

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1 73/1 數學系 譚必信 教授 期刊論文 發佈 On the daulity operator of a convex cone , [73-1] ：On the daulity operator of a convex cone期刊論文On the daulity operator of a convex coneTam, Bit-shun淡江大學數學學系New York : Elsevier Inc.Linear Algebra and Its Applications 64, pp.33-56Let C be a convex set in Rn. For each yϵC, the cone of C at y, denoted by cone(y, C), is the cone {α(x − y): α ⪖ 0 and xϵC}. If K is a cone in Rn, we shall denote by K∗ its dual cone and by F(K) the lattice of faces of K. Then the duality operator of K is the mapping View the MathML source given by View the MathML source. Properties of the duality operator dK of a closed, pointed, full cone K have been studied before. In this paper, we study dK for a general cone K, especially in relation to dcone(y, K), where yϵK. Our main result says that, for any closed cone K in Rn, the duality operator dK is injective (surjective) if and only if the duality operator dcone(y, K) is injective (surjective) for each vector yϵK ∼ [K ∩ (− K)]. In the last part of the paper, we obtain some partial results on the problem of constru
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