Let \({\mathcal {M}}\) be a \(\sigma\)-finite von Neumann algebra, equipped with a normal faithful state \(\varphi\), and let \({\mathcal {A}}\) be maximal subdiagonal subalgebra of \({\mathcal {M}}\) and \(1\le p<\infty\). We prove a Beurling–Blecher–Labuschagne type theorem for \({{\mathcal {A}}}\)-invariant subspaces of Haagerup noncommutative \(L^p({{\mathcal {A}}})\) and give a characterization of outer operators in Haagerup noncommutative \(H^{p}\)-spaces associated with \({{\mathcal {A}}}\).

中文翻译：

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Haagerup非交换$$ L ^ p $$ L p空间的Beurling–Blecher–Labuschagne型定理

令\（{\ mathcal {M}} \）为\（\ sigma \）有限的冯·诺依曼代数，并配备了正常的忠实状态\（\ varphi \），并令\（{\ mathcal {A}} \）是\（{\ mathcal {M}} \）和\（1 \ le p <\ infty \）的最大子对角子代数。我们证明了Haagerup非交换\（L ^ p（{^ {mathcal {A}}}）\）\（{{\ mathcal {A}}} \）-不变子空间的Beurling–Blecher–Labuschagne型定理，并给出与（（{{\ mathcal {A}}} \）相关的Haagerup非交换\（H ^ {p} \）-空间中外部算子的刻画。