Piecewise -homomorphisms and Jordan maps on C-algebras and factor von Neumann algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00323414" target="_blank" >RIV/68407700:21230/18:00323414 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.056" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.12.056</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2017.12.056" target="_blank" >10.1016/j.jmaa.2017.12.056</a>

Result language
angličtina
Original language name
Piecewise *-homomorphisms and Jordan maps on C*-algebras and factor von Neumann algebras
Original language description
We investigate maps between C*-algebras that are well behaved with respect to mutually commuting elements. We contribute to the Mackey-Gleason problem by showing that any continuous bijection between self-adjoint parts of C*-algebras that preserves triple product (a, b) -> aba, and is linear on commutative subspaces, is already linear. This allows us to describe such maps as direct differences of linear Jordan isomorphisms. We shall show that any weak*-continuous bijection between positive invertible elements of von Neumann factors (of dimension at least 9) that preserves products of commuting elements in both directions is of the form a -> e(Psi(log a))theta(a(c)), where theta is a linear Jordan *-isomorphism, c nonzero real number and Psi is a hermitian continuous functional. In a similar way we describe the same type of bicontinuous maps between unitary groups of von Neumann factors. General form of the above mentioned maps on C*-algebras is also presented. (C) 2017 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA17-00941S" target="_blank" >GA17-00941S: Topological and geometrical properties of Banach spaces and operator algebras II</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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