Kaplansky Density and Kadison Transitivity Theorems for Irreducible Representations of Real C^-Algebras  

作　　者：Jeffrey L.BOERSEMA 

机构地区：[1]Department of Mathematics,Seattle University,Seattle,WA 98122,USA

出　　处：《Acta Mathematica Sinica,English Series》2007年第10期1827-1832,共6页数学学报（英文版）

摘　　要：We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C＊-algebra on a real Hilbert space. Specifically, if a C＊-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.

关 键 词：real C＊-algebra irreducible ＊ representation TRANSITIVITY 

分 类 号：O177.5[理学—数学]