Convergence field of Abel's summation method

Rok, strany: 2012, 525 - 530

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 $S$.

ISO 690:

Letavaj, P. 2012. Convergence field of Abel's summation method. In Mathematica Slovaca, vol. 62, no.3, pp. 525-530. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0027-8

APA:

Letavaj, P. (2012). Convergence field of Abel's summation method. Mathematica Slovaca, 62(3), 525-530. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0027-8