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A letter concerning Leonetti's paper 'Continuous Projections onto Ideal Convergent Sequences'
- Publication Year :
- 2018
-
Abstract
- Leonetti proved that whenever $${\mathcal {I}}$$ is an ideal on $${\mathbb {N}}$$ such that there exists an uncountable family of sets that are not in $${\mathcal {I}}$$ with the property that the intersection of any two distinct members of that family is in $${\mathcal {I}}$$ , then the space $$c_{0,{\mathcal {I}}}$$ of sequences in $$\ell _\infty $$ that converge to 0 along $${\mathcal {I}}$$ is not complemented. We provide a shorter proof of a more general fact that the quotient space $$\ell _\infty / c_{0,{\mathcal {I}}}$$ does not even embed into $$\ell _\infty $$ .
- Subjects :
- Mathematics::Functional Analysis
Applied Mathematics
010102 general mathematics
46B20, 46B26 (primary), and 40A35 (secondary)
Space (mathematics)
Quotient space (linear algebra)
01 natural sciences
Functional Analysis (math.FA)
010101 applied mathematics
Combinatorics
Mathematics - Functional Analysis
Mathematics (miscellaneous)
FOS: Mathematics
Uncountable set
Ideal (ring theory)
Family of sets
0101 mathematics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....5fa019c0c3d830a49febe8530acc1ac5