There exists a real hereditarily indecomposable Banach space X = X(C) (resp. X = X(H)) such that the algebra L(X)/S(X) is isomorphic to C (resp. to the quaternionic division algebra H). Up to isomorphism, X(C) has exactly two complex structures, which are conjugate, totally incomparable, and both hereditarily indecomposable. So there exist two Banach spaces… (More)
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