ANGULAR DERIVATIVES OF HOLOMORPHIC MAPS IN INFINITE DIMENSIONS

Let H be a complex Hilbert space and let L(H, H) be the complex Banach space of all bounded linear operators from H to H with the operator n orm. In the generalized right half-planes and the unit balls contained in H and L(H, H), infinite-dimensional angular sets are defined, vari ous new generalizations of the classical Pick-Julia theorem to infinit e dimensions are proved, and conditions of Caratheodory-Fan type, guar anteeing the existence of angular limits and angular derivatives of ho lomorphic maps of these generalized right half-planes and unit balls, are established. (C) 1996 Academic Press, Inc.