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On the canonical embedding of a JB*‐triple into its bidual
Author(s) -
Isidro José M.
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700193
Subject(s) - mathematics , embedding , lie group , automorphism , pure mathematics , holomorphic function , combinatorics , artificial intelligence , computer science
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 ( B E ) → G ( B E ∗ ∗)between the corresponding real Banach Lie groups of holomorphic automorphisms of their respective open unit balls B E and B E ∗ ∗, the image J [ G ( B E ) ]being a closed (though not a direct) Lie subgroup of G ( B E ∗ ∗) .
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