A generalization of a theorem of Tatchell
Author:
Niranjan Singh
Journal:
Proc. Amer. Math. Soc. 70 (1978), 49-56
MSC:
Primary 40G99
DOI:
https://doi.org/10.1090/S0002-9939-1978-0487556-6
MathSciNet review:
487556
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Abstract | References | Similar Articles | Additional Information
Abstract: Necessary and sufficient conditions for to be summable
, whenever
is convergent, have been obtained. The sufficiency part of this result has also been improved.
- [1] G. H. Hardy, Divergent series, Oxford Univ. Press, London, 1949. MR 0030620 (11:25a)
- [2] M. W. Orlicz, Beitrage zur Theorie der Orthogonalentwicklungen. II, Studia Math. 1 (1929), 241-255.
- [3] J. B. Tatchell, A note on a theorem by Bosanquet, J. London Math. Soc. 29 (1954), 207-211. MR 0060611 (15:697f)
- [4] -, On some integral transforms, Proc. London Math. Soc. 3 (1953), 257-267. MR 0056727 (15:118f)
- [5] P. Dienes, The Taylor series, Dover, New York, 1957, p. 396. MR 0089895 (19:735d)
- [6] H. H. Körle, Über Unsteige absolute Riesz-Summujung. I, II, Math. Ann. 176 (1968), 45-52; ibid. 177 (1968), 230-234.
- [7] J. S. Ratti, Tauberian theorems for absolute summability, Proc. Amer. Math. Soc. 18 (1967), 775-781. MR 0216202 (35:7037)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1978-0487556-6
Keywords:
summability,
Banach space,
linear functionals and Riesz means
Article copyright:
© Copyright 1978
American Mathematical Society