Summability of subsequences and rearrangements of sequences

Author:
Thomas A. Keagy

Journal:
Proc. Amer. Math. Soc. **72** (1978), 492-496

MSC:
Primary 40C05

DOI:
https://doi.org/10.1090/S0002-9939-1978-0509240-2

MathSciNet review:
509240

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Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions have been given that require a matrix *A* to have the property that every sequence *x* with a finite limit point have a subsequence *y* such that each finite limit point of *x* is a limit point of *Ay*. In this paper, we show that these conditions may be weakened and obtain an analog in which ``subsequence'' is replaced with ``rearrangement".

**[1]**R. P. Agnew,*Summability of subsequences*, Bull. Amer. Math. Soc.**50**(1944), 596-598. MR**6**, 46. MR**0010616 (6:46a)****[2]**R. C. Buck,*A note on subsequences*, Bull. Amer. Math. Soc.**49**(1943), 898-899. MR**5**, 117. MR**0009208 (5:117b)****[3]**-,*An addendum to*``*A note on subsequences*,'' Proc. Amer. Math. Soc.**7**(1956), 1074-1075. MR**18**, 478. MR**0081983 (18:478g)****[4]**D. F. Dawson,*Summability of subsequences and stretchings of sequences*, Pacific J. Math.**44**(1973), 455-460. MR**47**#5478. MR**0316930 (47:5478)****[5]**J. A. Fridy,*Summability of rearrangements of sequences*, Math. Z.**143**(1975), 187-192. MR**52**#3772. MR**0382890 (52:3772)****[6]**I. J. Maddox,*A Tauberian theorem for subsequences*, Bull. London Math. Soc.**2**(1970), 63-65. MR**41**#5836. MR**0261220 (41:5836)****[7]**T.A. Keagy,*Summability of certain category two classes*, Houston J. Math.**3**(1977), 61-65. MR**0425410 (54:13365)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1978-0509240-2

Keywords:
Rearrangement,
regular summability method

Article copyright:
© Copyright 1978
American Mathematical Society