TY - JOUR
AU - Patterson, Richard F.
PY - 2004/06/30
Y2 - 2022/05/26
TI - Four dimensional characterization of bounded double sequences
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 35
IS - 2
SE -
DO - 10.5556/j.tkjm.35.2004.214
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/214
SP - 129-134
AB - In 1945 Brudno presented the following important theorem: If $A$ and $B$ are regular summability matrix methods such that every bounded sequence summed by $A$ is also summed by $B$, then it is summed by $B$ to the same value. R. G. Cooke suggested that a simpler proof would be desirable. Petersen presented such a proof. The goal of the paper is to present an accessible multidimensional analog of Brudno theorem for double sequences using four dimensional matrix transformations.
ER -