A Beurling–Blecher–Labuschagne type theorem for Haagerup noncommutative Lp spaces

Let M be a σ -finite von Neumann algebra, equipped with a normal faithful state φ , and let A be maximal subdiagonal subalgebra of M and 1 ≤ p < ∞ . We prove a Beurling–Blecher–Labuschagne type theorem for A -invariant subspaces of Haagerup noncommutative L p ( A ) and give a characterization of outer operators in Haagerup noncommutative H p -spaces associated with A .