Matrix summability of unbounded sequences
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- by J. DeFranza and K. Zeller PDF
- Proc. Amer. Math. Soc. 115 (1992), 171-175 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 171-175
- MSC: Primary 40C05; Secondary 40G05, 46A45
- DOI: https://doi.org/10.1090/S0002-9939-1992-1094498-1
- MathSciNet review: 1094498