On strictly singular nonlinear centralizers

Abstract: We show that is the only Banach space with unconditional basis that satisfies the equation . 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 for , Tsirelson and Schlumprecht spaces and their duals, as well as certain super-reflexive variations of these spaces. In the last section, we give estimates of the projection constants of certain finite-dimensional twisted sums of Kalton–Peck type. [Copyright &y& Elsevier]