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Triangulations of Operators with Two-Isometric Liftings
Integral Equations and Operator Theory ( IF 0.8 ) Pub Date : 2021-02-01 , DOI: 10.1007/s00020-021-02625-9
Witold Majdak , Laurian Suciu

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.



中文翻译:

具有两个等距提升的算子的三角剖分

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。

更新日期:2021-02-01
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