How large is the space of almost convergent sequences?

How large is the space of almost convergent sequences?

We consider the subspaces c, cˆ, S of ℓ∞, where cˆ consists of almost convergent sequences, and S consists of sequences whose arithmetic means of consecutive terms are convergent. We know that c⊂cˆ⊂S. We examine the largeness of c in cˆ, cˆ in S and S in ℓ∞ or the differences of these sets. We will...

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Veröffentlicht in:Journal of mathematical analysis and applications 2023-10, Vol.526 (1), p.127258, Article 127258
1. Verfasser: Nowakowski, Piotr
Format: Artikel
Sprache:eng
Schlagworte:
Algebrability
Banach limits
Measure of families of sequences
Porosity
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Zusammenfassung:We consider the subspaces c, cˆ, S of ℓ∞, where cˆ consists of almost convergent sequences, and S consists of sequences whose arithmetic means of consecutive terms are convergent. We know that c⊂cˆ⊂S. We examine the largeness of c in cˆ, cˆ in S and S in ℓ∞ or the differences of these sets. We will do that from the viewpoints of porosity, algebrability and measure.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127258