On the core of a cone-preserving map

doi:10.2307/2154729

淡江大學機構典藏 > 理學院 > 應用數學與數據科學學系 > 期刊論文 > Item 987654321/41195

請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/41195

題名:	On the core of a cone-preserving map
作者:	譚必信;Tam, Bit-shun;Schneider, Hans
貢獻者:	淡江大學數學學系
日期:	1994-06
上傳時間:	2010-01-28 06:54:06 (UTC+8)
出版者:	Providence: American Mathematical Society (AMS)
摘要:	This is the third of a sequence of papers in an attempt to study the Perron-Frobenius theory of a nonnegative matrix and its generalizations from the cone-theoretic viewpoint. Our main object of interest here is the core of a cone-preserving map. If A is an n x n real matrix which leaves invariant a proper cone K in R" , then by the core of A relative to K , denoted by cokk{A) , we mean the convex cone \|~)~, A'K. It is shown that when coreK(A) is polyhedral, which is the case whenever K is, then cotck(A) is generated by the distinguished eigenvectors of positive powers of A . The important concept of a distinguished /1-invariant face is introduced, which corresponds to the concept of a distinguished class in the nonnegative matrix case. We prove a significant theorem which describes a one-to-one correspondence between the distinguished ^-invariant faces of K and the cycles of the permutation induced by A on the extreme rays of core^f/l), provided that the latter cone is nonzero, simplicial. By an interplay between cone-theoretic and graph-theoretic ideas, the extreme rays of the core of a nonnegative matrix are fully described. Characterizations of A"-irreducibility or A-primitivity of A are also found in terms of cotzk(A) . Several equivalent conditions are also given on a matrix with an invariant proper cone so that its spectral radius is an eigenvalue of index one. An equivalent condition in terms of the peripheral spectrum is also found on a real matrix A with the Perron-Schaefer condition for which there exists a proper invariant cone K suchthat core^(^) is polyhedral, simplicial, or a single ray. A method of producing a large class of invariant proper cones for a matrix with the Perron-Schaefer condition is also offered.
關聯:	Transactions of the American Mathematical Society 343(2), pp.479-524
DOI:	10.2307/2154729
顯示於類別:	[應用數學與數據科學學系] 期刊論文

文件中的檔案:

檔案	描述	大小	格式	瀏覽次數
0002-9947_343(2)p479-524.pdf		5909Kb	Adobe PDF	722	檢視/開啟
On the core of a cone-preserving map.pdf		5549Kb	Adobe PDF	1	檢視/開啟

在機構典藏中所有的資料項目都受到原著作權保護.

TAIR相關文章

資料載入中.....