Summability of subsequences and rearrangements of sequences

Keagy, Thomas A.

doi:10.1090/S0002-9939-1978-0509240-2

Summability of subsequences and rearrangements of sequences
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by Thomas A. Keagy PDF

Proc. Amer. Math. Soc. 72 (1978), 492-496 Request permission

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".

References

Ralph Palmer Agnew, Summability of subsequences, Bull. Amer. Math. Soc. 50 (1944), 596–598. MR 10616, DOI 10.1090/S0002-9904-1944-08201-3
R. Creighton Buck, A note on subsequences, Bull. Amer. Math. Soc. 49 (1943), 898–899. MR 9208, DOI 10.1090/S0002-9904-1943-08051-2
R. Creighton Buck, An addendum to “A note on subsequences”, Proc. Amer. Math. Soc. 7 (1956), 1074–1075. MR 81983, DOI 10.1090/S0002-9939-1956-0081983-2
David F. Dawson, Summability of subsequences and stretchings of sequences, Pacific J. Math. 44 (1973), 455–460. MR 316930
John A. Fridy, Summability of rearrangements of sequences, Math. Z. 143 (1975), no. 2, 187–192. MR 382890, DOI 10.1007/BF01187062
I. J. Maddox, A Tauberian theorem for subsequences, Bull. London Math. Soc. 2 (1970), 63–65. MR 261220, DOI 10.1112/blms/2.1.63
Thomas A. Keagy, Summability of certain category two classes, Houston J. Math. 3 (1977), no. 1, 61–65. MR 425410