Hilbert spaces and C*-algebras are not finitely concrete

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F23%3APU146983" target="_blank" >RIV/00216305:26210/23:PU146983 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14310/23:00134041
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0022404922002432" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0022404922002432</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2022.107245" target="_blank" >10.1016/j.jpaa.2022.107245</a>

Result language
angličtina
Original language name
Hilbert spaces and C*-algebras are not finitely concrete
Original language description
We show that no faithful functor from the category of Hilbert spaces with injective linear contractions into the category of sets preserves directed colimits. Thus Hilbert spaces cannot form an abstract elementary class, even up to change of language. We deduce an analogous result for the category of commutative unital C*- algebras with *-homomorphisms. This implies, in particular, that this category is not axiomatizable by a first-order theory, a strengthening of a conjecture of Bankston. (C) 2022 Elsevier B.V. All rights reserved.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10100 - Mathematics

Project
<a href="/en/project/GA19-00902S" target="_blank" >GA19-00902S: Injectivity and Monads in Algebra and Topology</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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