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Inclusion relations for Riesz typical means

Published online by Cambridge University Press:  24 October 2008

A. Jakimovski  and
J. Tzimbalario
A. Jakimovski
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
J. Tzimbalario
Affiliation:
Department of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel
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Abstract

Necessary and sufficient conditions for sequence-to-sequence or sequence-to-function summability method to include (R, λ, α), when 1 < α ≤ 2, are given. Also, for suitably restricted sequences λ, necessary and sufficient conditions for a series-to-sequence or series-to-function summability method to include (R, λ, α) for 1 < α ≤ 2 are given. These results are obtained by showing that a certain sequence {δj} (j ≥ 0) is a Schauder-basis in Rλα(N) for each α, 1 < α ≤ 2.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 3 , November 1972 , pp. 417 - 423
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

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