A Letter Concerning Leonetti’s Paper ‘Continuous Projections Onto Ideal Convergent Sequences

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 c 0 , I of sequences in ℓ ∞ that converge to 0 along I is not complemented. We provide a shorter proof of a more general fact that the quotient space ℓ ∞ / c 0 , I does not even embed into ℓ ∞ .