Pontriagin空间上算子的交换性  

On the Commutativty of Operators on Pontrjagin Spaces

作　　者：杨海涛[1] 苏桂贤[1] 

机构地区：[1]广东海洋大学数学系

出　　处：《数学学报（中文版）》2006年第2期451-458,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：证明了:当Pontrjagin空间上的正规算子A没有零性不变子空间时,Putnam- Fuglede定理成立;当正规算子A有零性不变子空问时,通过构造反例说明此时Putnam- Fuglede定理不成立,并对Π1空间上算子相关的交换性条件进行了讨论,得到了Π1空间上算子代数的二次交换定理．We show that the Putnam-Fuglede theorem holds, if the normal operator A on the Pontrjagin spaces has not a neutral invariant subspace. If the normal operator A has a neutral invariant subspace, then we use examples to show that the Putnam-Fuglede theorem is not hold. We also study the conditions for commutativity of operators on the Ⅱ1 spaces, and prove the double commutant theorem for the operator algebras on the Ⅱ1 spaces.

关 键 词：PONTRJAGIN空间 正规算子 Putnam—Fuglede定理 

分 类 号：O177.5[理学—数学]