Dye's theorem for tripotents in von Neumann algebras and JBW*-triples
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00355025" target="_blank" >RIV/68407700:21230/21:00355025 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s43037-021-00134-w" target="_blank" >https://doi.org/10.1007/s43037-021-00134-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s43037-021-00134-w" target="_blank" >10.1007/s43037-021-00134-w</a>
Alternative languages
Result language
angličtina
Original language name
Dye's theorem for tripotents in von Neumann algebras and JBW*-triples
Original language description
We study morphisms of the generalized quantum logic of tripotents in JBW*-triples and von Neumann algebras. Especially, we establish a generalization of celebrated Dye's theorem on orthoisomorphisms between von Neumann lattices to this new context. We show the existence of a one-to-one correspondence between the following maps: (1) quantum logic morphisms between the posets of tripotents preserving reflection u -> -u (2) maps between triples that preserve tripotents and are real linear on sets of elements with bounded range tripotents. In a more general description we show that quantum logic morphisms on structure of tripotents are given by a family of Jordan *-homomorphisms on Peirce 2-subspaces. By examples we demonstrate optimality of the results. Besides we show that the set of partial isometrics with its partial order and orthogonality relation is a complete Jordan invariant for von Neumann algebras.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Banach Journal of Mathematical Analysis
ISSN
2662-2033
e-ISSN
1735-8787
Volume of the periodical
15
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
18
Pages from-to
2-19
UT code for WoS article
000652224100001
EID of the result in the Scopus database
2-s2.0-85106306422