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Linear maps preserving idempotence on nest algebras - MaRDI portal

Linear maps preserving idempotence on nest algebras (Q1780292)

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scientific article; zbMATH DE number 2174194
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Linear maps preserving idempotence on nest algebras
scientific article; zbMATH DE number 2174194

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    Linear maps preserving idempotence on nest algebras (English)
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    7 June 2005
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    The authors produce several theorems regarding the structure of linear preservers on nest algebras over Hilbert space. Specifically, they consider (nonsurjective, surjective, surjective bounded, and surjective weakly continuous) rank-one preservers. As a consequence, they also consider linear maps on atomic nests, and show that a bijective, weakly continuous linear map preserves idempotents if and only if it is Jordan, which in turn is equivalent to being an automorphism or an anti-automorphism.
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    nest algebras
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    rank-one operators
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    idempotent operators
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    Jordan isomorphisms
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