For every compact metric space K there exists a reflexive Banach space whose Calkin algebra is isomorphic to C(K), with stability under products, Holder continuity of diagonals, rigidity determining the topology of K, and classification of ideals.
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Operator Algebras of Bourgain Delbaen Spaces: Realization, Rigidity, and Ideal Structure
For every compact metric space K there exists a reflexive Banach space whose Calkin algebra is isomorphic to C(K), with stability under products, Holder continuity of diagonals, rigidity determining the topology of K, and classification of ideals.