The compact operators on c₀ as a Calkin algebra

For a Banach space X, let L(X) denote the algebra of all bounded linear operators on X and let K(X) denote the compact operator ideal in L(X). The quotient algebra L(X)/K(X) is called the Calkin algebra of X, and it is denoted Cal(X). We prove that the unitization of K(c₀) is isomorphic as a Banach algebra to the Calkin algebra of some Banach space ZK(c₀). This Banach space is an Argyros-Haydon sum (⊕ₙ₌₁^∞ Xₙ)AH of a sequence of copies Xₙ of a single Argyros-Haydon space XAH, and the external versus the internal Argyros-Haydon construction parameters are chosen from disjoint sets.