Banach spaces with very few operators

Journal article, 2016

If X is a separable infinite dimensional Banach space, the only general operators which are known to exist on X are of the form I+K, where is a scalar and K is a compact operator (obtained as a limit in norm of finite rank operators). We present here a remarkable construction, due to S. Argyros and R. Haydon, of spaces on which every operator can be written as the sum of a scalar operator and a compact operator.