The paper deals with bounded linear operators T on a complex Hilbert space \({\mathcal {H}}\) which have 2-isometric liftings S on a Hilbert space \({\mathcal {K}}\) containing \({\mathcal {H}}\) as a closed subspace. We investigate three types of such liftings, and for each type we describe in detail the corresponding operators T by the \(2\times 2\) upper triangular block matrices. The entries of those matrices are expressed by operators which belong to certain classes of A-contractions for some positive operators A on \({\mathcal {H}}\). We also refer to the expansive operators with such liftings, as well as to Brownian isometric or quasi-Brownian unitary liftings.

与纸张的交易界线性算Ť上的复杂的Hilbert空间\（{\ mathcal {H}} \） ，其具有2等距运油š上的Hilbert空间\（{\ mathcal {K}} \）含有\（{ \ mathcal {H}} \）作为封闭子空间。我们研究了这种提升的三种类型，对于每种类型，我们通过\（2 × 2）上三角块矩阵来详细描述相应的算符T。这些矩阵的项由属于某些类别A-压缩的算子表示，对于\（{\ mathcal {H}} \）上的某些正算子A。我们还提到具有这种提升的广义算子，以及布朗等距或准布朗单一提升。