Year: 2026
Type: article
Abstract: Given any compact Hausdorff space X , we present a simple proof that a continuous function $$g\in \mathcal {C}(X)$$ g ∈ C ( X ) can be uniformly approximated on X by elements of some linear subspace $$\mathcal {L}\subset \mathcal {C}(X)$$ L ⊂ C ( X ) , if and only if g can be pointwise approximated on X by some equibounded sequence in $$\mathcal {L}$$ L . Moreover, given any compactum $$K\subset \mathbb {C}$$ K ⊂ C , we also show that every $$f\in \mathcal {C}(K)$$ f ∈ C ( K ) can be uniformly approximated by rational functions (without poles on K ), if and only if the complex conjugate $$w\mapsto \overline{w}$$ w ↦ w ¯ can be pointwise approximated by functions holomorphic on K (no equibounded hypothesis required).
Authors: Eduardo S. Zeron, Jesús Emmanuel Castillo
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Award: G7262698406
OpenAlex ID: W7160779987