Banach spaces with small spaces of operators

Abstract

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.

Cited by in corpus (2)

• K-theory for algebras of operators on Banach spaces
• Uniqueness of unconditional bases in Banach spaces