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On admissible topologies in JB*‐triples
Author(s) -
Isidro José M.
Publication year - 2015
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.201400132
Subject(s) - mathematics , surjective function , network topology , bounded function , unit sphere , regular polygon , norm (philosophy) , holomorphic function , pure mathematics , topology (electrical circuits) , discrete mathematics , combinatorics , mathematical analysis , computer science , geometry , political science , law , operating system
Given a complex JB*‐triple X , we define and study admissible topologies on X , i.e., locally convex topologies τ on X coarser than the norm topology, invariant under the group of surjective linear isometries of X , and such that the triple product is jointly τ − τ ‐continuous on bounded subsets of X . As a consequence of the joint τ − τ ‐continuity of the triple product, all holomorphic automorphisms g ∈ Aut ( B ) of the open unit ball B ⊂ X are homeomorphisms of ( B , τ | B ) and the natural action( a , z ) ↦ g a ( z )is jointly τ − τ ‐continuous on B × B .