On the structure of the cone of positive operators
學年 80
學期 2
出版（發表）日期 1992-04-01
作品名稱 On the structure of the cone of positive operators
作品名稱（其他語言）
著者 Tam, Bit-Shun
單位 淡江大學數學學系
出版者 Philadelphia: Elsevier Inc.
著錄名稱、卷期、頁數 Linear Algebra and Its Applications 167, pp.65-85
摘要 If K1 is a proper cone in Rn1 and K2 is a proper cone in Rn2, then, as is well known, the set π(K1, K2), which consists of all n2 x n1 real matrices which take K1 into K2, forms a proper cone in the space Rn2, n1. In this paper a study of this cone is made, with particular emphasis on its faces and duality operator. A face of π(K1, K2) is called simple if it is composed of all matrices in π(K1, K2) which take some fixed face of K1 into some fixed face of K2. Maximal faces of π(K1, K2) are characterized as a particular kind of simple faces. Relations between the duality operator of π(K1, K2) and those of K1 and K2 are obtained. Among many other results, it is proved that dπ(K1, K2), the duality operator of π(K1, K2), is injective if and only if dK2 is injective and each face of π(K1, K2) is an intersection of simple faces. Two open questions are posed.
關鍵字
語言 en
ISSN 0024-3795
期刊性質 國外
收錄於 SCI
產學合作
通訊作者 Tam, Bit-Shun
審稿制度
國別 USA
公開徵稿
出版型式 紙本
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