On strictly singular nonlinear centralizers

We show that c0c0 is the only Banach space with unconditional basis that satisfies the equation Ext(X,X)=0Ext(X,X)=0. This partially improves an old result by Kalton and Peck. We prove that the Kalton–Peck maps are strictly singular on a number of sequence spaces, including ℓpℓp for 0