Let \({\mathcal {M}}\) be a diffuse von Neumann algebra with a faithful normal semi-finite trace \(\tau \), and let E be a symmetric quasi-Banach space. Then for any Orlicz function \(\varphi \), we can define the noncommutative Calderón–Lozanovskiĭ spaces \(E_\varphi ({\mathcal {M}})\). These spaces share many properties with their classical counterparts. In particular, new multiplication operator spaces and complex interpolation spaces of such spaces are given under a wide range of conditions. Moreover, letting \({\mathcal {A}}\) be a maximal subdiagonal algebra of \({\mathcal {M}}\), we introduce the noncommutative Calderón–Lozanovskiĭ–Hardy spaces \(H^\varphi ({\mathcal {A}})\) and transfer the recent results of the noncommutative Hardy spaces to the noncommutative Calderón–Lozanovskiĭ–Hardy spaces.

假设\（{\ mathcal {M}} \）是具有忠实的标准半有限迹\（\ tau \）的扩散冯·诺伊曼代数，并且E是对称的拟Banach空间。然后，对于任何Orlicz函数\（\ varphi \），我们都可以定义非交换Calderón–Lozanovski \空间\（E_ \ varphi（{\ mathcal {M}}）\）。这些空间与经典空间共享许多属性。特别地，在宽范围的条件下给出了新的乘法算子空间和这种空间的复数插值空间。此外，令\（{\ mathcal {A}} \）为\（{\ mathcal {M}} \）的最大对角线代数，我们引入非交换Calderón–Lozanovskiĭ–Hardy空间\（H ^ \ varphi（{\ mathcal {A}}）\）并将非可交换Hardy空间的最新结果转移到非可交换Calderón–Lozanovskiĭ–Hardy空间。