A sufficient condition for a regular matrix to sum a bounded divergent sequence
HTML articles powered by AMS MathViewer
- by A. Mary Tropper
- Proc. Amer. Math. Soc. 4 (1953), 671-677
- DOI: https://doi.org/10.1090/S0002-9939-1953-0056724-2
- PDF | Request permission
References
- Richard G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan & Co., Ltd., London, 1950. MR 0040451 S. Mazur and W. Orlicz, Sur les méthodes linéaires de sommation, C. R. Acad. Sci. Paris vol. 196 (1933) pp. 32-34.
- V. Darevsky, On intrinsically perfect methods of summation, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 10 (1946), 97–104 (Russian, with English summary). MR 0016145
- J. D. Hill, Some properties of summability. II, Bull. Amer. Math. Soc. 50 (1944), 227–230. MR 10000, DOI 10.1090/S0002-9904-1944-08117-2
- Albert Wilansky, A necessary and sufficient condition that a summability method be stronger than convergence, Bull. Amer. Math. Soc. 55 (1949), 914–916. MR 32024, DOI 10.1090/S0002-9904-1949-09307-2
- Karl Zeller, Allgemeine Eigenschaften von Limitierungsverfahren, Math. Z. 53 (1951), 463–487 (German). MR 39824, DOI 10.1007/BF01175646
- G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190. MR 27868, DOI 10.1007/BF02393648
- G. G. Lorentz, Direct theorems on methods of summability, Canad. J. Math. 1 (1949), 305–319. MR 32023, DOI 10.4153/cjm-1949-028-6
- Ralph Palmer Agnew, Convergence fields of methods of summability, Ann. of Math. (2) 46 (1945), 93–101. MR 11334, DOI 10.2307/1969149
- Albert Wilansky, An application of Banach linear functionals to summability, Trans. Amer. Math. Soc. 67 (1949), 59–68. MR 32025, DOI 10.1090/S0002-9947-1949-0032025-7
- Albert Wilansky, Norms of matrix type for the spaces of convergent and bounded sequences, Proc. Amer. Math. Soc. 2 (1951), 738–741. MR 44027, DOI 10.1090/S0002-9939-1951-0044027-X
- Ralph Palmer Agnew, A simple sufficient condition that a method of summability be stronger than convergence, Bull. Amer. Math. Soc. 52 (1946), 128–132. MR 14488, DOI 10.1090/S0002-9904-1946-08522-5
- A. Brudno, Summation of bounded sequences by matrices, Rec. Math. [Mat. Sbornik] N.S. 16(58) (1945), 191–247 (Russian, with English summary). MR 0012340
Bibliographic Information
- © Copyright 1953 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 4 (1953), 671-677
- MSC: Primary 40.0X
- DOI: https://doi.org/10.1090/S0002-9939-1953-0056724-2
- MathSciNet review: 0056724