A non-zero symmetric sequence ideal E ⊆ c_0 is a continuous linear image of C_p(X) only if E = c_0, so proper ideals such as (ℓ_q)_p never appear.
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Continuous Linear Surjections from $C_p(X)$ onto Symmetric Sequence Ideals in $c_0$
A non-zero symmetric sequence ideal E ⊆ c_0 is a continuous linear image of C_p(X) only if E = c_0, so proper ideals such as (ℓ_q)_p never appear.