Nonlinear maps on von Neumann algebras preserving the star order

DOI10.1080/03081087.2012.721363zbMath1282.46053OpenAlexW2041378311MaRDI QIDQ2850994

Jan Hamhalter, Martin Bohata

Publication date: 1 October 2013

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081087.2012.721363

zbMATH Keywords

von Neumann algebra\(C^\ast\)-algebrastar ordernonlinear maps preserving the star order

Mathematics Subject Classification ID

General theory of von Neumann algebras (46L10) Linear operators on Banach algebras (47B48) Automorphisms of selfadjoint operator algebras (46L40)

Related Items (6)

Star order on operator and function algebras and its nonlinear preservers ⋮ Star order automorphisms on the poset of type 1 operators ⋮ Star order on JBW algebras ⋮ Star order and partial isometries in \(C^\ast\)-algebras ⋮ Minus partial order and linear preservers ⋮ Automorphisms of spectral lattices of positive contractions on von Neumann algebras

Cites Work

• Star partial order on \(B(H)\)
• Automatic continuity of biorthogonality preservers between compact \(C^*\)-algebras and von Neumann algebras
• Orthogonality preservers in C\(^*\)-algebras, JB\(^*\)-algebras and JB\(^*\)-triples
• Automorphisms of \(B(H)\) with respect to minus partial order
• Disjointness preserving operators on \(C^*\)-algebras
• Maps on quantum observables preserving the Gudder order
• On the geometry of projections in certain operator algebras
• A note on the star order in Hilbert spaces
• Star order on operator and function algebras
• Natural structures on semigroups with involution

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