A Beurling–Blecher–Labuschagne type theorem for Haagerup noncommutative L^p spaces

Bekjan T.N. Raikhan M.
April 2021 Birkhauser

Banach Journal of Mathematical Analysis
2021 #15 Issue 2

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.

Beurling’s theorem , Haagerup noncommutative H^p-space , Invariant subspace , Outer operator , Subdiagonal algebras

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College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China
Astana IT University, Nur-Sultan, 010000, Kazakhstan

College of Mathematics and Systems Science
Astana IT University

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