C~*-代数之间正算子列的收敛性

Convergence of sequence of positive operators between C~*-algebras

引入了C~*-代数A与B之间的广义-同态φ_n:A→B与φ:A→B在点α处的三种偏差:δ_n^(1) (α),δ_n^(2)(α)与δ_n^(3)(α),证明了若E■A且对任—x∈E,■δ_n^(i)(x)=0,则对任—x∈C~*(E)有■δ_n^(i)(x)=0,特别■φ_n(x)=φ(x),(i=2,3)。作为推论得到了古典逼近论的Korovkin定理。

The three errors δ_n^(1)(a),δ_n^(2)(a),δ_n^(3)(a) of the generalized~*-homomor- phism φ_n to φ from C~*-algebra A into B at the point a are introduced.And it is proved that if E■A,i=2,3,■δ_n^(i)(x)=0,for x in E,then for all x in C~*(E)(C~*-subalgebras generated by E),■δ_n^(i)(x)=0,in particular,■φ_n(x)=φ(x).As a corrollary,the classical korovkin's Approxima tion Theorem is obtained.