Abstract
Kadison's transitivity theorem implies that, for irreducible representations of \cstar algebras, every invariant linear manifold is closed. It is known that CSL algebras have this property if, and only if, the lattice is hyperatomic (every projection is generated by a finite number of atoms). We show several other conditions are equivalent, including the condition that every invariant linear manifold is singly generated. \par We show that two families of norm closed operator algebras have this property. First, let
Citation
Allan Donsig. Alan Hopenwasser. David R. Pitts. "Automatic closure of invariant linear manifolds for operator algebras." Illinois J. Math. 45 (3) 787 - 802, Fall 2001. https://doi.org/10.1215/ijm/1258138151
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