J 2023

Hilbert spaces and C*-algebras are not finitely concrete

LIEBERMAN, Michael Joseph, Jiří ROSICKÝ and Sébastien Bernard VASEY

Basic information

Original name

Hilbert spaces and C*-algebras are not finitely concrete

Authors

LIEBERMAN, Michael Joseph (840 United States of America), Jiří ROSICKÝ (203 Czech Republic, guarantor, belonging to the institution) and Sébastien Bernard VASEY (756 Switzerland, belonging to the institution)

Edition

Journal of Pure and Applied Algebra, Elsevier, 2023, 0022-4049

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Netherlands

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 0.800 in 2022

RIV identification code

RIV/00216224:14310/23:00134041

Organization unit

Faculty of Science

DOI

UT WoS

000892539300014

Keywords in English

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

Tags

Tags

International impact, Reviewed
Změněno: 9/1/2023 10:16, Mgr. Marie Šípková, DiS.

Abstract

V originále

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.

Links

GA19-00902S, research and development project
Name: Injektivita a monády v algebře a topologii
Investor: Czech Science Foundation