## 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)

### MSC:

 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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