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We give a new more explicit proof of a result by Kalton & Lancien statingthat on each Banach space with an unconditional basis not isomorphic to aHilbert space there exists a generator of a holomorphic semigroup which doesnot have maximal regularity. In particular, we show that there always exists aSchauder basis (f_m) such that the generator is a Schauder multiplierassociated to the sequence (2^m). Moreover, we show that maximal regularitydoes not extrapolate: we construct consistent holomorphic semigroups (T_p(t))on L^p for p in (1, \infty) which have maximal regularity if and only if p = 2.These assertions were both open problems. Our approach is completely differentthan the one of Kalton & Lancien. We use the characterization of maximalregularity by R-sectoriality for our construction.

The Kalton-Lancien Theorem Revisited: Maximal Regularity does not extrapolate