A Banach space in which every injective operator is surjective

We construct an infinite dimensional Banach space of continuous functions C(K) such that every one-to-one operator on C(K) is onto.

💡 Research Summary

The paper addresses a long‑standing question in Banach space theory: does there exist an infinite‑dimensional Banach space on which every injective bounded linear operator is automatically surjective? Such spaces are called Hopfian Banach spaces. While many classical spaces (ℓ₁, ℓ₂, C