In this paper, we discuss measure theoretic characterizations for Moore-Penrose inverse of Lambert conditional operators, denoted by (M_wEM_u)^†, in some operator classes on L²(Σ) such as p-hyponormal, centered, n-normal, bi-normal, partial isometry, quasinilpotent and EP operator. Moreover, we prove some basic results on (M_wEM_u)^†, for instance, triple reverse order law and lower and upper bounds for the numerical range of (M_wEM_u)^†. Also, we investigate some results concerning the Fuglede-Putnam property of \(\tilde T,{\tilde T^\dagger },\widetilde {{T^\dagger }}\) and some correlations between these types of operators.

在本文中，我们将讨论用于测量兰伯特条件运算符，用（的Moore-Penrose逆理论表征中号_瓦特EM _ù）^†，在一些操作符类大号²（Σ）如p -hyponormal，居中，Ñ -正常，双正态，部分等距，拟幂等和EP运算符。此外，我们证明了关于（M _w EM _u）^†的一些基本结果，例如，三重逆序定律以及（M _w EM _u）^†的数值范围的上下限。此外，我们研究了有关\（\ tilde T，{\ tilde T ^ \ dagger}，\ widetilde {{T ^ \ dagger}} \）的Fuglede-Putnam属性的一些结果以及这些类型的运算符之间的一些相关性。