Publication detail

Hilbert spaces and C*-algebras are not finitely concrete

LIEBERMAN, M. VASEY, S. ROSICKÝ, J.

Original Title

Hilbert spaces and C*-algebras are not finitely concrete

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

LIEBERMAN, M.; VASEY, S.; ROSICKÝ, J.

Released

1. 4. 2023

Publisher

ELSEVIER

Location

AMSTERDAM

ISBN

0022-4049

Periodical

JOURNAL OF PURE AND APPLIED ALGEBRA

Year of study

227

Number

4

State

Kingdom of the Netherlands

Pages count

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"
}