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Banach spaces with small spaces of operators

W. T. Gowers·B. Maurey
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Abstract

For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. 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.

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W. T. Gowers, B. Maurey. 1994-07-20. Banach spaces with small spaces of operators. https://arxiv.org/abs/math/9407209

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