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A note on summability factors

Published online by Cambridge University Press:  26 February 2010

L. S. Bosanquet  and
J. B. Tatchell
L. S. Bosanquet
Affiliation:
University College, London.
J. B. Tatchell
Affiliation:
University College, London.
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Our main object in this note is to establish (Theorem 1) a necessary and sufficient condition to be satisfied by a sequence {εn} so that a series Σ an εnmay be summable | A |whenever the series Σanis summable (C, — 1). We suppose that an and εn are complex numbers. The condition is unchanged if the an are restricted to be real, but our proof is adapted to the case where they may be complex. Theorem 1 has been quoted by Bosanquet and Chow [12] in order to fill a gap in the theory of summability factors. We also obtain some related results, which are discussed in the Appendix.

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Type
Research Article
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Mathematika , Volume 4 , Issue 1 , June 1957 , pp. 25 - 40
Copyright
Copyright © University College London 1957

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