An infinite dimensional extension of the Pick-Julia theorem is used to derive the conditions of Carathéodory type which guarantee the existence of angular limits and angular derivatives for holomorphic maps of infinite dimensional bounded symmetric homogeneous domains in -algebras and in complex Hilbert spaces. The case of operator-valued analytic maps is considered and examples are given.
Da un'estensione di dimensione infinita del teorema di Pick-Julia vengono dedotte condizioni, «alla Carathéodory», sufficienti per l'esistenza di limiti angolari e derivate angolari per applicazioni olomorfe di domini limitati omogenei simmetrici in algebre ed in spazi di Hilbert. Si considerano alcuni esempi e si studiano funzioni analitiche i cui valori sono degli operatori.
@article{RLIN_1994_9_5_1_43_0,
author = {Kazimierz W\l odarczyk},
title = {Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
volume = {5},
year = {1994},
pages = {43-53},
zbl = {0802.46060},
mrnumber = {1273892},
language = {en},
url = {http://dml.mathdoc.fr/item/RLIN_1994_9_5_1_43_0}
}
Włodarczyk, Kazimierz. Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 5 (1994) pp. 43-53. http://gdmltest.u-ga.fr/item/RLIN_1994_9_5_1_43_0/
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