A letter concerning Leonetti's paper 'Continuous Projections onto Ideal Convergent Sequences'

0498574 - MÚ 2020 RIV CH eng J - Journal Article
Kania, Tomasz
A letter concerning Leonetti's paper 'Continuous Projections onto Ideal Convergent Sequences'.
Results in Mathematics. Roč. 74, č. 1 (2019), č. článku 12. ISSN 1422-6383. E-ISSN 1420-9012
R&D Projects: GA ČR(CZ) GA17-27844S
Institutional support: RVO:67985840
Keywords : convergence along an ideal * complemented subspace * Phillips-Sobczyk theorem * Grothendieck space
OECD category: Pure mathematics
Impact factor: 1.162, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00025-018-0936-0

Leonetti proved that whenever I is an ideal on N such that there exists an uncountable family of sets that are not in I with the property that the intersection of any two distinct members of that family is in I, then the space c0, I of sequences in 8 that converge to 0 along I is not complemented. We provide a shorter proof of a more general fact that the quotient space 8/ c0, I does not even embed into l(infinity).
Permanent Link: http://hdl.handle.net/11104/0290899