Invariant subspaces for H2 spaces of σ-finite algebras
Abstract
We show that a Beurling type theory of invariant subspaces of noncommutative H
2
spaces
holds true in the setting of subdiagonal subalgebras of σ-finite von Neumann algebras. This
extends earlier work by Blecher and Labuschagne on finite algebras, and complements more
recent contributions in this regard by Bekjan and Chen, Hadwin and Shen in the finite setting,
and Sager in the semifinite setting.
We also introduce the notion of an analytically conditioned algebra, and go on to show that
in the class of analytically conditioned algebras this Beurling type theory is part of a list of
properties which all turn out to be equivalent to the maximal subdiagonality of the given algebra.
This list includes a Gleason–Whitney type theorem, as well the pairing of the unique normal
state extension property and an L
2
density condition
URI
http://hdl.handle.net/10394/20670http://dx.doi.org/10.1112/blms.12009
http://onlinelibrary.wiley.com/doi/10.1112/blms.12009/abstract