Banach spaces with small spaces of operators. (English) Zbl 0876.46006

For a certain class of algebras \({\mathcal A}\) we give a method for constructing Banach spaces \(X\) such that every operator on \(X\) is close to an operator in \({\mathcal A}\). This is used to produce spaces with a small amount of structure. We present several applications. Amongst them are constructions of a new prime Banach space, a space isomorphic to its subspaces of codimension two but not to its hyperplanes and a space isomorphic to its cube but not to its square.
Reviewer: B.Maurey (Paris)


46B03 Isomorphic theory (including renorming) of Banach spaces
46B20 Geometry and structure of normed linear spaces
47A53 (Semi-) Fredholm operators; index theories
47A99 General theory of linear operators
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