Banach spaces with small spaces of operators
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1994
 arXiv:
 arXiv:math/9407209
 Bibcode:
 1994math......7209G
 Keywords:

 Mathematics  Functional Analysis;
 46B