Complex interpolation of quasi-Banach spaces with an A-convex containing space
Complex interpolation of general couples (X0, X1) of quasi-Banach spaces has been considered by several authors [8], [11], [16]. The first approach was made by Rivi6re in his thesis [16] and recently it has been developed by Cwikel, Milman and Sagher in [8], where some new interpolation results have been obtained. See also [9] and [17]. These authors have used in the classical construction of Calder6n (see [4] or [3]) the space ~ of all functions J(z) =~=lfk(z)xk, where x ~ X0 n X 1 and f~E A (S, C), the class of scalar valued functions analytic on the strip S={z: 0 < R e z < l } and continuous and bounded on S. As a result, a quasi-normed space of analytic functions is obtained in which the quasi-norm IL" IL~ on ~ is the one introduced by Calder6n [4], i.e.