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• W4318052111 startingPage "127044" @default.
• W4318052111 abstract "A bijective map between specific structures in operator algebras is called a piecewise isomorphism if it preserves products of commuting elements in both directions. We shall show that any bicontinuous piecewise isomorphism between positive cones of invertible elements in von Neumann algebras or between unitary groups of von Neumann algebras can be described in terms of the following parameters: (i) Jordan *-isomorphism between given algebras (ii) one fixed central element in domain (or range) algebra (iii) a hermitian linear map from one algebra into the center of the other one. Especially, in case of factors any piecewise isomorphism between unitary groups is a Jordan *-isomorphism or Jordan *-isomorphism composed with inversion. This extends hitherto known results from von Neumann factors to general von Neumann algebras and brings new Jordan invariants of operator structures." @default.
• W4318052111 created "2023-01-26" @default.
• W4318052111 creator A5091615681 @default.
• W4318052111 date "2023-07-01" @default.
• W4318052111 modified "2023-09-23" @default.
• W4318052111 title "Maps preserving products of commuting elements in von Neumann algebras" @default.
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• W4318052111 doi "https://doi.org/10.1016/j.jmaa.2023.127044" @default.
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