Abstract
Let M be a von Neumann algebra with a faithful, normal, tracial state τ \tau and H ∞ {H^\infty } be a finite, maximal, subdiagonal algebra of M. Every left- (or right-) invariant subspace with respect to H ∞ {H^\infty } in the noncommutative Lebesgue space L p ( M , τ ) , 1 ⩽ p > ∞ {L^p}(M,\tau ),1 \leqslant p > \infty , is the closure of the space of bounded elements it contains.
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