2026/07/16 by Antonio Acuaviva, Pablo Acuaviva
#math.FA
Let \mathscrA(X) and \mathscrK(X) denote the ideals of approximable and compact operators on a Banach space X, respectively. We construct a unital Banach algebra A of density character \mathfrak c=2ℵ0, with exactly one non-zero proper closed two-sided ideal, such that, for every Banach space X, the algebra A is isomorphic to neither \mathscrB(X)/\mathscrA(X) nor \mathscrB(X)/\mathscrK(X). Thus A is not a Calkin algebra under either of the two customary conventions.