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Convergence field of Abel’s summation method

✍ Scribed by Peter Letavaj


Book ID
111877334
Publisher
SP Versita
Year
2012
Tongue
English
Weight
144 KB
Volume
62
Category
Article
ISSN
0139-9918

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✦ Synopsis


Let F (A) denote the set of all bounded sequences summable by Abel's method. It is known, that F (A) is a linear subspace of the linear metric space (S, ρ) of all bounded sequences endowed with the sup metric. It is shown in [KOSTYRKO, P.: Convergence fields of regular matrix transformations 2, Tatra Mt. Math. Publ. 40 (2008), 143-147] that the convergence field of a regular matrix transformation is a σ-porous set. We show that F (A) is very porous in S.


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