Detail publikačního výsledku

Hilbert spaces and C*-algebras are not finitely concrete

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Originální název

Hilbert spaces and C*-algebras are not finitely concrete

Anglický název

Hilbert spaces and C*-algebras are not finitely concrete

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Hilbert space; C?-algebra; Faithful functor preserving directed  colimits

Klíčová slova v angličtině

Hilbert space; C?-algebra; Faithful functor preserving directed  colimits

Autoři

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Rok RIV

2024

Vydáno

01.04.2023

Nakladatel

ELSEVIER

Místo

AMSTERDAM

ISSN

0022-4049

Periodikum

JOURNAL OF PURE AND APPLIED ALGEBRA

Svazek

227

Číslo

4

Stát

Nizozemsko

Strany počet

9

URL

http://www.sciencedirect.com/science/article/pii/S0022404922002432

BibTex

@article{BUT181494,
  author="Michael Joseph {Lieberman} and Sebastien {Vasey} and Jiří {Rosický}",
  title="Hilbert spaces and C*-algebras are not finitely concrete",
  journal="JOURNAL OF PURE AND APPLIED ALGEBRA",
  year="2023",
  volume="227",
  number="4",
  pages="9",
  doi="10.1016/j.jpaa.2022.107245",
  issn="0022-4049",
  url="http://www.sciencedirect.com/science/article/pii/S0022404922002432"
}