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Summability of alterations based on stretchings of sequences. (English) Zbl 0551.40003

Sufficient conditions on a matrix A are known which guarantee for every sequence x the existence of a submatrix B of A and stretching y of x such that each finite limit point of x is a limit point of By. In Section 2 of this paper, the author extends this result to show y may be selected such that Ay exists. This extension is then used to obtain an independent proof of a limit point preserving theorem for subsequences, originally proved by the author [Proc. Am. Math. Soc. 72, 492-496 (1978; Zbl 0425.40002)]. An analogue to the above mentioned extension for \(G\in\)- stretchings of a sequence x is obtained in Section 3, which provides implications for studying the summability transforms of stretchings for certain types of matrices and leads to an improvement of D. F. Dawson’s ”Copy Theorem”. In addition, characterizations of several well-known sequence spaces are also obtained.
Reviewer: Y.Sitaraman

MSC:

40C05 Matrix methods for summability
46A45 Sequence spaces (including Köthe sequence spaces)

Citations:

Zbl 0425.40002
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