Invariant inner product in spaces of holomorphic functions on bounded symmetric domains.

Arazy, Jonathan; Upmeier, Harald

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The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in $J^{*}$ -algebras. Since $J^{*}$ -algebras are natural generalizations of $C^{*}$ -algebras, $B^{*}$ -algebras, $J C^{*}$ -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.