Lyapunov Convexity Theorem for von Neumann Algebras and Jordan Operator Structures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F21%3A00346259" target="_blank" >RIV/68407700:21230/21:00346259 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00009-020-01624-1" target="_blank" >https://doi.org/10.1007/s00009-020-01624-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00009-020-01624-1" target="_blank" >10.1007/s00009-020-01624-1</a>
Alternative languages
Result language
angličtina
Original language name
Lyapunov Convexity Theorem for von Neumann Algebras and Jordan Operator Structures
Original language description
We establish Lyapunov type theorems on automatic convexity of various affine transformations of the set of extreme points of important convex sets (closed unit ball, positive part of the closed unit ball, state space) appearing in the theory of von Neumann algebras and more general operator structures. Among others, we have shown that every bounded finitely additive measure mu :P(M)-> X, where P(M) is a projection lattice of a von Neumann algebra M with no sigma -finite direct summand, and X is a normed space with weak separable dual, has a convex range. Similar result is obtained for non sigma -finite JW factor. Further results along this line are proved for weak* continuous countably dimensional affine maps on closed unit balls of nonatomic JBW triples and on positive parts of nonatomic von Neumann algebras and JBW algebras.
Czech name
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Czech description
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Classification
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
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
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
MEDITERRANEAN JOURNAL OF MATHEMATICS
ISSN
1660-5446
e-ISSN
1660-5454
Volume of the periodical
18
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
25
Pages from-to
1-25
UT code for WoS article
000594162200002
EID of the result in the Scopus database
2-s2.0-85095979753