K. Wlodarczyk et A. Szalowska, ANGULAR DERIVATIVES OF HOLOMORPHIC MAPS IN INFINITE DIMENSIONS, Journal of mathematical analysis and applications, 204(1), 1996, pp. 1-28
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.