ON REDUCTIVE OPERATORS AND OPERATOR ALGEBRAS
Copyright policy )ON REDUCTIVE OPERATORS AND OPERATOR ALGEBRAS
We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a nonzero compact operator. We deduce a number of corollaries which apply to the reductivity problem.Bibliography: 20 titles.
Structure theory of linear operators, Linear symmetric and selfadjoint operators (unbounded), Invariant subspaces of linear operators, General theory of von Neumann algebras, Linear operators in algebras, Hermitian and normal operators (spectral measures, functional calculus, etc.)
Structure theory of linear operators, Linear symmetric and selfadjoint operators (unbounded), Invariant subspaces of linear operators, General theory of von Neumann algebras, Linear operators in algebras, Hermitian and normal operators (spectral measures, functional calculus, etc.)
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