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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Matrix summability of unbounded sequences


Authors: J. DeFranza and K. Zeller
Journal: Proc. Amer. Math. Soc. 115 (1992), 171-175
MSC: Primary 40C05; Secondary 40G05, 46A45
MathSciNet review: 1094498
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Abstract: A well-known result of Mazur and Orlicz states that a matrix method strictly stronger than convergence sums not only bounded sequences but unbounded sequences. We consider the question of whether a matrix method strictly stronger than convergence will also sum a sequence with series terms (differences) constituting an unbounded sequence. This is equivalent to the series to sequence convergence domain of the matrix containing an unbounded sequence. A simple criterion is given showing in many cases the answer is positive. Counterexamples of three types are considered; triangles that are not perfect, perfect row finite matrices, and perfect triangles.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1094498-1
PII: S 0002-9939(1992)1094498-1
Article copyright: © Copyright 1992 American Mathematical Society