We apply the complex method of interpolation to families of infinite-dimensional, separable Hilbert spaces, and obtain a detailed description of the structure of the interpolation spaces, by means of a unique "extremal" operator-valued, analytic function. We use these interpolation techniques to give a different proof, under weaker assumptions, of a theorem of A. Devinatz concerning the factorization of positive, infinite-rank, operator-valued functions.
Interpolation and factorization of operators / S. Bloom; A. Tabacco; M. Vignati. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 102(1988), pp. 567-576.