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
• DOI: 10.2478/s12175-012-0027-8

✦ 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.