A geometric characterisation of real C^(*)-algebras  

作　　者：Cho-Ho Chu 

机构地区：[1]School of Mathematical Sciences,Queen Mary University of London,London E 14NS,UK

出　　处：《Science China Mathematics》2023年第10期2277-2292,共16页中国科学：数学（英文版）

基　　金：supported by the Engineering and Physical Sciences Research Council,UK(Grant No.EP/R044228/1).

摘　　要：We characterise the positive cone of a real C^(*)-algebra geometrically.Given an open coneΩin a real Banach space V,with the closureΩ,we show thatΩis the interior of the positive cone of a unital real C^(*)-algebra if and only if it is a Finsler symmetric cone with an orientable extension,which is equivalent to the condition that V is,in an equivalent norm,the Hermitian part of a unital real C^(*)-algebra with the positive coneΩ.

关 键 词：real C^(*)-algebra Banach manifold Finsler symmetric cone Jordan algebra 

分 类 号：O15[理学—数学]