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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on invariant subspaces for finite maximal subdiagonal algebras


Author: Kichi-Suke Saito
Journal: Proc. Amer. Math. Soc. 77 (1979), 348-352
MSC: Primary 46L10; Secondary 46L50
DOI: https://doi.org/10.1090/S0002-9939-1979-0545594-X
MathSciNet review: 545594
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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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DOI: https://doi.org/10.1090/S0002-9939-1979-0545594-X
Keywords: Subdiagonal algebras, invariant subspaces, von Neumann algebras
Article copyright: © Copyright 1979 American Mathematical Society