Complexification of operators between L _p -spaces

摘要

During the X ELAM I reported about various results which were obtained jointly with A. Defantin [2] and [3] concerning the following problem:For q,p E [1 , 00] and a continuous linear operator T : L:(p) - L:(v) (arbitrary measures p and v)consider the complexification TC : Lf (p) - L?? {v) defined by ,TC(f + ig) : = Tf + iTg