Abstract
AbstractWe give a universal formula describing derivation operators on a
Hilbert space for a large class of interpolation methods. It is based on a simple new technique on
“critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in
particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real J-method. Previously,
such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial
derivations whose values on the critical points grow to infinity as slowly as we wish.
Publisher
Springer Science and Business Media LLC
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