Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Absolute summability matrices that are stronger than the identity mapping


Author: J. A. Fridy
Journal: Proc. Amer. Math. Soc. 47 (1975), 112-118
DOI: https://doi.org/10.1090/S0002-9939-1975-0350249-7
MathSciNet review: 0350249
Full-text PDF

Abstract | References | Additional Information

Abstract: The main result gives a simple column-sum property which implies that the matrix $ A$ maps $ {l_A}$ properly into $ {l^1}$, i.e., $ {l^1} \subsetneqq {A^{ - 1}}[{l^1}]$. Also, the means of Nörlund, Euler-Knopp, Taylor, and Hausdorff are investigated as mappings of $ {l^1}$ into itself.


References [Enhancements On Off] (What's this?)

  • [1] R. P. Agnew, Euler transformations, Amer. J. Math. 66 (1944), 313-338. MR 6, 46. MR 0010618 (6:46c)
  • [2] R. P. Agnew, A simple sufficient condition that a method of summability be stronger than convergence, Bull. Amer. Math. Soc. 52 (1946), 128-132. MR 7, 292. MR 0014488 (7:292h)
  • [3] V. F. Cowling, Summability and analytic continuation, Proc. Amer. Math. Soc. 1 (1950), 536-542. MR 12, 91. MR 0036326 (12:91d)
  • [4] J. A. Fridy, Properties of absolute summability matrices, Proc. Amer. Math. Soc. 24 (1970), 583-585. MR 42 #724. MR 0265815 (42:724)
  • [5] -, Mercerian-type theorems for absolute summability, Portugal. Math. 33 (1974), 141-145. MR 0361523 (50:13968)
  • [6] G. H. Hardy, Divergent series, Clarendon Press, Oxford, 1949. MR 11, 25. MR 0030620 (11:25a)
  • [7] K. Knopp and G. G. Lorentz, Beiträge zur absoluten Limitierung, Arch. Math. 2 (1949), 10-16. MR 11, 346. MR 0032790 (11:346i)
  • [8] W. Meyer-König, Untersuchungen über einige verwandte Limitierungsverfahren, Math. Z. 52 (1949), 257-304. MR 11, 242. MR 0032021 (11:242b)
  • [9] R. E. Powell and S. M. Shah, Summability theory and applications, Van Nostrand Reinhold, London, 1972.


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0350249-7
Keywords: $ l - l$ matrix, sum-preserving, Nörlund means, Euler-Knopp means, Taylor method, Hausdorff means, quasi-Hausdorff means, regular mass function
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society