Remark on Co-Null Matrices
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 105-107
Voir la notice de l'article provenant de la source Cambridge University Press
A well-known theorem of Copping [2] states that a conservative matrix with a bounded left inverse cannot evaluate a bounded divergent sequence. (Definitions are given in the next paragraph.) A proof was given by Parameswaran [3, Theorem 6. 1], using only the simplest Banach-space ideas. This proof, however, is valid only for co-regular methods; it was stated in [3, Theorem 6. 2] that a co-null matrix cannot have a bounded left inverse, but the proof there given is incorrect, as it uses for co-null methods a theorem established only for co-regular. It would be desirable to have a short independent proof of this known result, which excludes co-null matrices from consideration in Copping' s theorem. This is furnished by the slightly more general result given below.
Macphail, M. S. Remark on Co-Null Matrices. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 105-107. doi: 10.4153/CMB-1965-013-2
@article{10_4153_CMB_1965_013_2,
author = {Macphail, M. S.},
title = {Remark on {Co-Null} {Matrices}},
journal = {Canadian mathematical bulletin},
pages = {105--107},
year = {1965},
volume = {8},
number = {1},
doi = {10.4153/CMB-1965-013-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-013-2/}
}
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[4] 4. Wilansky, A. and Zeller, K., The inverse matrix in summability: reversible matrices, Journal of the London Mathematical Society, 32(1957), 397-408. Google Scholar
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