A note on invariant subspaces for finite maximal subdiagonal algebras

Saito, Kichi-Suke

doi:10.1090/S0002-9939-1979-0545594-X

A note on invariant subspaces for finite maximal subdiagonal algebras
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Proc. Amer. Math. Soc. 77 (1979), 348-352 Request permission

Abstract:

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

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