幂等算子组的联合谱

Joint spectrum of tuples of idempotents

通过将问题简化为计算一个投影算子P和一个幂等算子Q的联合谱,得到两个幂等算子的联合谱.首先计算P和Q的值域投影的联合谱这一特殊情况,接着计算一般情况下的联合谱.最后讨论了I、P、Q的联合谱,通过这个特殊的联合谱,对P+Q和P-Q的谱进行了刻画.

By reducing the problem to the calculation of the joint spectrum of a projection P and an idempotent Q,the joint spectrum of two idempotents is obtained.First the joint spectrum of P and the range projection of Q,which is of a special case,was calculated and then the joint spectrum in general case.The joint spectrum of I,P,Q is also discussed.Through this special case of joint spectrum,the spectrum of P+Q and P-Q are characterized.