On the canonical embedding of a JB‐triple into its bidual

We prove that the canonical embedding J:E→E∗∗ of a JB*‐triple E into its bidual E∗∗ extends uniquely to a manifold embedding J:G(BE)→G(BE∗∗) between the corresponding real Banach Lie groups of holomorphic automorphisms of their respective open unit balls BE and BE∗∗, the image J[G(BE)] being a close...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 291; no. 17-18; pp. 2578 - 2584
Main Author Isidro, José M.
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.12.2018
Subjects
17C65
32M15
57T15
58B12; Secondary: 14M17
Automorphisms
Banach–Lie groups
bounded symmetric domains
Embedding
holomorphic automorphisms
JB‐triples
Lie groups
Primary: 46G20
Subgroups
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Summary:We prove that the canonical embedding J:E→E∗∗ of a JB*‐triple E into its bidual E∗∗ extends uniquely to a manifold embedding J:G(BE)→G(BE∗∗) between the corresponding real Banach Lie groups of holomorphic automorphisms of their respective open unit balls BE and BE∗∗, the image J[G(BE)] being a closed (though not a direct) Lie subgroup of G(BE∗∗).
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201700193