摘要
在文[1]中定义上乘运算,半同态,从而定义了Banach~*上代数。本文进一步讨论Banach~*上代数的上理想与上子代数。将它们置于空间偶对中考虑,给出了C~*上代数A与其对偶B~*代数A~*(及C~*代数A与其对偶B~*上代数A~*)的上理想与子代数,上子代数与理想之间的对偶关系,进一步明确了在拓扑结构下这种代数结构的对称性。
Comultiplication and semihomomorphism were defined in [1],and then Banach* coalgebra was defined. In this paper,the coideals and cosubalgebras in Banach* coalgebra are futher discussed. And they are under the consideration a pair of space and it's dual. The coideal and subalgebra of A,C* coalgebra and those of A,B* algebra are given and B* algebra pairs up with A, C* coalgebra. Besides , the pairing relation between cosubalgebra and ideal is offered. Thus the symmetry among the previous algebra structures under the topology structure is further understood.
关键词
上理想
上子代数
理想
子代数
coideal cosubalgebra ideal subagelbra topology compatible with dual (A, A~*)
