有限套代数上保3-单位积的线性映射

Linear Mappings of Preserving 3-unit Products on Finite Nest Algebras

设A,B分别是B(H)和B(K)的子代数,且I∈A,φ是A到B的线性映射,称φ从A到B是保3-单位积的,如果对任意的X,Y,Z∈A且XYZ=I,有φ(X)φ(Y)φ(Z)=I。该文主要证明以下结果,设H是Hilbert空间,N是H上的有限套,φ是有限套代数algN到自身保3-单位积的有界线性双射,且φ(I)=I,则φ是空间自同构。

Le tand be a sub-algebra of and with.We say that a linear mapping is a preserving 3-unite products if for any X,Y,Z∈A with XYZ=I.In this paper,we obtain the following results: Let H be a Hilbert space,is a finite nest about H;be a continuous linear bijective mapping of preserving 3-unite products from the finite nest Algebra onto itself and,then is a spatial isomorphism.