Characterizations of certain classes of hereditary *-subalgebras
Characterizations of certain classes of hereditary *-subalgebras
复制标题
某些类别的遗传*-子代数的特征
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
Masaharu Kusuda
中科院分区：
文献类型：
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作者：
Masaharu Kusuda
利用范数1从C*-代数的包络von Neumann代数到遗传C*-子代数的包络von Neumann代数的投影，刻画了C*-代数中的全遗传C*-子代数类和生成本质理想的遗传C *-子代数类.对于C*-动力系统（A，G，a），还证明了A的a-不变C*-子代数B是属于上述任一类的遗传C*-子代数当且仅当约化C* -交叉积B x，r G是约化C* -交叉积Ax，r G的遗传C* -子代数，与B属于同一类.此外，还观察到C*-交叉产物的类似结果。
This paper characterizes the class of full hereditary C*-subalgebras and the class of hereditary C*-subalgebras that generate essential ideals in a given C*-algebra in terms of a certain projection of norm one from the enveloping von Neumann algebra of the C*-algebra onto the enveloping von Neumann algebra of a hereditary C*-subalgebra. For a C*-dynamical system (A, G, a), it is also shown that an a-invariant C*-subalgebra B of A is a hereditary C*-subalgebra belonging to either of the above classes if and only if the reduced C* -crossed product B x ,r G is a hereditary C* -subalgebra, of the reduced C* -crossed product A x ,r G, belonging to the same class as B . Furthermore similar results for C*-crossed products are also observed.