The compact operators on $c_0$ 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 of a sequence of copies Xn of a single Argyros-Haydon space XAH, and the external versus the internal Argyros-Haydon con- struction parameters are chosen from disjoint sets.