On 𝒜-submodules for reflexive operator algebras
| Autor: | De Guang Han |
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| Rok vydání: | 1988 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 104:1067-1070 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/s0002-9939-1988-0969048-7 |
| Popis: | In [2] the authors described all weakly closed A \mathcal {A} -submodules of L ( H ) L\left ( H \right ) for a nest algebra A \mathcal {A} in terms of order homomorphisms of Lat A \mathcal {A} . In this paper we prove that for any reflexive algebra A \mathcal {A} which is σ \sigma -weakly generated by rank-one operators in A \mathcal {A} , every σ \sigma -weakly closed A \mathcal {A} -submodule can be characterized by an order homomorphism of Lat A \mathcal {A} . In the case when A \mathcal {A} is a reflexive algebra with a completely distributive subspace lattice and M \mathcal {M} is a σ \sigma -weakly closed ideal of A \mathcal {A} , we obtain necessary and sufficient conditions for the commutant of A \mathcal {A} modulo M \mathcal {M} to be equal to AlgLat M \mathcal {M} . |
| Databáze: | OpenAIRE |
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