On the inclusion of a bounded convergence field in the space of almost convergent sequences
1972 ◽
Vol 13
(1)
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pp. 82-90
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Keyword(s):
Let T = (tmn) be a regular matrix, and CTbe its bounded convergence field. Necessary and sufficient conditions for CT to contain the space of almost convergent sequences are well known. (See, e.g., [7, p.62]). G. M. Petersen has suggested as a problem for research the discovery of necessary and sufficient conditions for the reverse inclusion: When is CT contained in the space of almost convergent sequences? [7, p. 137, research problem 9]. In this paper we deal with this question in a more general context. First we need some notation.
2004 ◽
Vol 03
(02)
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pp. 207-217
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2013 ◽
Vol 88
(2)
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pp. 232-242
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2020 ◽
Vol 13
(5)
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pp. 1088-1096
2000 ◽
Vol 24
(8)
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pp. 533-538
1964 ◽
Vol 6
(4)
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pp. 161-168
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1996 ◽
Vol 54
(2)
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pp. 197-202
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1981 ◽
Vol 4
(1)
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pp. 155-164