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

Arazy, Jonathan; Upmeier, Harald

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The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of $C^{*}$ -algebras

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Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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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.

Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains

Kazimierz Włodarczyk (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of $J^{*}$ -algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.