TUHF代数上的Jordan映射

Jordan Maps on TUHF Algebras

设T是TUHF代数,B是有理数域Q上的代数,r是一个有理数,φ是从T到B上的双射,并且任给a,b∈T,都有φ(r(ab+ba))=r(φ(a)φ(b)+φ(b)φ(a)).本文研究了φ的可加性.证明了当T有不变投影或为标准TUHF时,φ是可加的.

Let T be a TUHF algebra, B is an associative algebra over the field Q of rational numbers and r∈Q. In this paper, the additivity of maps φ from T onto B is discussed, which is bijective and satisfies φ（r（ab＋ba））=r（φ（a）φ（b）＋φ（b）φ（a）） for all a,b∈T,If T is a standard TUHF algebra or T has an invariant projection, then φ is additive.