Mercerian Theorems for Beekmann Matrices
Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 83
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
A matrix $A=(a_{nk})$ is called {\it normal\/} if $a_{nk}=0$
for $k>n$ and $a_{nn}\neq 0$ for all $n$. Such a matrix has a normal inverse
$A^{-1}=(\alpha_{nk})$. If Ihe inverse $A^{-1}$ of a normal and regular
matrix $A$ satisfies the conditions $\alpha_{nk}\leq 0$ for $k0$ for all $n$, we call such a matrix a Beekmann matrix.
Beekmann introduced those matrices and proved that for such a matrix $A$,
the matrix $B=(I+\lambda A)/(1+\lambda)$ is Mercerian for $\lambda>-1$.
(I is the identity matrix.) This paper extends Beekmann's theorem to the case of $R_\beta$-Mercerian
matrices, $\beta>0$.
Classification :
40C05
@article{PIM_1987_N_S_41_55_a10,
author = {Vladeta Vu\v{c}kovi\'c},
title = {Mercerian {Theorems} for {Beekmann} {Matrices}},
journal = {Publications de l'Institut Math\'ematique},
pages = {83 },
publisher = {mathdoc},
volume = {_N_S_41},
number = {55},
year = {1987},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1987_N_S_41_55_a10/}
}
Vladeta Vučković. Mercerian Theorems for Beekmann Matrices. Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 83 . http://geodesic.mathdoc.fr/item/PIM_1987_N_S_41_55_a10/