Nonlinear centralizers in homology (Q2448328)

For any reasonable measure space, the function spaces \(L_p\) are in a natural way quasi-Banach modules over \(L_\infty\); most statements in this paper must be interpreted in this category. \textit{N. J. Kalton} [Mem. Am. Math. Soc. 385 (1988; Zbl 0658.46059)] showed that, if \(p,q\in(1,\infty)\) and \(p\neq q\), then every extension of \(L_p\) by \(L_q\) is trivial. This result is extended here to the range \((0,\infty)\). The proofs rely on a careful analysis of nonlinear centralizers and homology sequences.