A note on commutator estimates for interpolation methods



The aim of this note is to show how all the commutator estimates of two recent papers, by M. Cwikel, N. Kalton, M. Milman, and R. Rochberg and by N. Krugljak and M. Milman, can be considered as special cases of the method of couples of interpolators introduced by M. J. Carro, J. Cerdà and J. Soria, and also to show how the distance between orbits and the “Benson norm” considered by Krugljak and Milman can be extended, respectively, as a distance between the interpolators that appear in the general construction and as a constant that is finite when the interpolators satisfy the necessary cancellation property. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)