Four dimensional characterization of bounded double sequences

Authors

  • Richard F. Patterson

DOI:

https://doi.org/10.5556/j.tkjm.35.2004.214

Abstract

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.

Author Biography

Richard F. Patterson

Department of Mathematics and Statistics, University of North Florida Building 11 Jacksonville, Florida, 32224, U.S.A.

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Published

2004-06-30

How to Cite

Patterson, R. F. (2004). Four dimensional characterization of bounded double sequences. Tamkang Journal of Mathematics, 35(2), 129–134. https://doi.org/10.5556/j.tkjm.35.2004.214

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Section

Papers