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Operator algebras with
reducing invariant subspaces
Thomas Benton Hoover |
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Vol. 44 (1973), No. 1, 173–179
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Abstract |
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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 ℐ be the von Neumann algebra genenerated by the projections which commute with 𝒜. If ℐ is properly infinite, or it ℐ has a cyclic vector, then 𝒜 is self-adjoint. If ℐ has no direct summand which is abelian and of infinite uniform multiplicity, then ℐ is the commutant of 𝒜. |
Mathematical Subject Classification 2000
Primary: 47A15
Secondary: 46L15
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Milestones
Received: 29 September 1971
Published: 1 January 1973
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Authors |
| Thomas Benton Hoover | |
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