THE CONSERVATIVE MATRIX ON LOCALLY CONVEX SPACES

Let (X, τX) and (Y, τY) be locally convex spaces, c(X) and c(Y) the X-valued and Y-valued convergent sequence spaces, respectively, Aij ϵ L(X, Y) and A = (Aij) an operator-valued infinite matrix. In this paper, we characterize the matrix A = (Aij) which transforms c(X) into c(Y). As its applications...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 7; no. 2; pp. 283 - 291
Main Authors Junde, Wu, Dohan, Kim, Minhyung, Cho
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China (Taiwan) 01.06.2003
Subjects
Applied mathematics
College mathematics
Linear transformations
Mathematical sequences
Matrices
Topological spaces
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Summary:Let (X, τX) and (Y, τY) be locally convex spaces, c(X) and c(Y) the X-valued and Y-valued convergent sequence spaces, respectively, Aij ϵ L(X, Y) and A = (Aij) an operator-valued infinite matrix. In this paper, we characterize the matrix A = (Aij) which transforms c(X) into c(Y). As its applications, we introduce the chi function χ on locally convex spaces, and show that a conservative matrix is conull if and only if χ(A) = 0.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500575065