Let I⊆ P(ω) be a meager ideal. Then there are no continuous projections from ℓ∞ onto the set of bounded sequences which are I-convergent to 0. In particular, it follows that the set of bounded sequences statistically convergent to 0 is not isomorphic to ℓ∞.

Continuous projections onto ideal convergent sequences

Leonetti P
2018-01-01

Abstract

Let I⊆ P(ω) be a meager ideal. Then there are no continuous projections from ℓ∞ onto the set of bounded sequences which are I-convergent to 0. In particular, it follows that the set of bounded sequences statistically convergent to 0 is not isomorphic to ℓ∞.
2018
2018
asymptotic density zero sets; complementability; I-convergent sequence; I-maximal almost disjoint family; Meager ideal
Leonetti, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2142094
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