环面代数扩张的同态

本文研究了环面代数(即C(T2))扩张问同态的性质．设E1和E2为环面代数通过K的本质酉扩张,φ,ψ:E1→E2为单同态,若φ,ψ在半群V(E1)及商代数上导出的映射一致,则φ与ψ是近似酉等价的．这里K为可分的无限维复Hilbert空间上的紧算子全体构成的C*-代数,V(E1)为E1的矩阵代数中投影的Murray-von Neumann等价类构成的交换半群．

Homomorphisms from Extensions of Torus Algebra

Homomorphisms between the extensions of torus algebra are considered. Suppose that E1 and E2 are two extensions of C(T2) by K., andφ,ψare injective homomorphisms from E1 into E2. We prove that such two homomorphisms are approximately unitarily equivalent when they have the same induced maps on the invariant V(E1) and the quotient algebra, where K is the C*-algebra of all compact operators on a separable infinite dimensional Hilbert space and V(E1) is the commutative semigroup consisting of the Murray-von Neumann equivalence classes of projections in matrices over E1..