Vol. 44, No. 1, 1973

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Operator algebras with reducing invariant subspaces

Thomas Benton Hoover

Vol. 44 (1973), No. 1, 173–179

A weakly closed algebra of operators on a Hilbert space is reductive if every subspace which is invariant for the algebra reduces. If 𝒜 is a reductive algebra, let be the von Neumann algebra genenerated by the projections which commute with 𝒜. If is properly infinite, or it has a cyclic vector, then 𝒜 is self-adjoint. If has no direct summand which is abelian and of infinite uniform multiplicity, then is the commutant of 𝒜.

Mathematical Subject Classification 2000
Primary: 47A15
Secondary: 46L15
Received: 29 September 1971
Published: 1 January 1973
Thomas Benton Hoover