CAJ | 학술논문

讨论了希尔伯特空间上的两个不同的幂等算子P、Q的组合aP＋bQ-cPQ的可逆性问题，利用幂等算子的性质和空间分解的技巧证明了aP＋bQ-cPQ的可逆性与系数的选取无关，其中a，b，c∈C，ab≠0，a＋b-c≠0．而且构造反例说明该结果不能推广到aP＋bQ-cPQ-dQP的情形．
토론료희이백특공간상적량개불동적멱등산자P、Q적조합aP＋bQ-cPQ적가역성문제，이용멱등산자적성질화공간분해적기교증명료aP＋bQ-cPQ적가역성여계수적선취무관，기중a，b，c∈C，ab≠0，a＋b-c≠0．이차구조반례설명해결과불능추엄도aP＋bQ-cPQ-dQP적정형．
Discussed the problem of invertibility of combinations of two different idempotent operators P,Q on a Hilbert space. The invertibility of aP + bQ-cPQ are independent choice of coefficients, where a, b, c ∈ C ,ab ≠ 0 ,a +b ≠c which was proved by using the properties of idempotent operators and the techniques of space decomposition. Moreover, some counter examples were constructed to denote that the result can not be generalized to the case aP + bQ-cPQ-dQP .