On BV-Reversible matrices

Year 1988, Volume: 37 , - , 01.01.1988

J.ı. Okutoyı

https://doi.org/10.1501/Commua1_0000000555

Abstract

İn 1932, S. Banacii stated that if A is a re\'ersibie matrİK, then the System of egnations
k=o a‘.nk-^Xk,
has a unique solution given by X = vl + By, where B — is the uniqııe right inverse cf A,
By = s Yk k=o
co
I , vGc, xgc4^ and v — (v )* e In 1953 MacPhail shovzed that v need n=o ‘ a o not belong to by giving a simple reversible matrix with v ubounded.
It is the purpose of this paper to extend Banach’s work on c-reversible matrices to bv-re- versible matrİces and construct matrices which are bv-rever»ible matrices but not c-reversible; the first one with v bounded and the second one with v unbounled.
Notations: s; c; bv; bs; l^,; Ca i 0; 8; X* will denote the set of ali sequences; convergent secjuenccs; sequences of bounded variation that is, sequences such that S | | 00
k=o
and lim X]j exists; bounded series, that is, sequences x such that
’eo
n sup I S X]j I
k=o
00; bounded sequences; convergence domain, that
is, cx = {xes; Axec}; S (1. 1, ...), 8*^ X* the continuous dual of X respectively.
n=o (0,0,...,0,1,0;...)

Keywords

Reversible matrices, Mathematics, Statistics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi