Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00130024" target="_blank" >RIV/00216224:14310/23:00130024 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/2203.12087.pdf" target="_blank" >https://arxiv.org/pdf/2203.12087.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2022.107209" target="_blank" >10.1016/j.jpaa.2022.107209</a>

Result language
angličtina
Original language name
Monadic forgetful functors and (non-)presentability for C⁎- and W⁎-algebras
Original language description
We prove that the forgetful functors from the categories of C⁎- and W⁎-algebras to Banach ⁎-algebras, Banach algebras or Banach spaces are all monadic, answering a question of J.Rosický, and that the categories of unital (commutative) C⁎-algebras are not locally-isometry ℵ0-generated either as plain or as metric-enriched categories, answering a question of I. Di Liberti and Rosický. We also prove a number of negative presentability results for the category of von Neumann algebras: not only is that category not locally presentable, but in fact its only presentable objects are the two algebras of dimension ≤1. For the same reason, for a locally compact abelian group G the category of G-graded von Neumann algebras is not locally presentable.
Czech name
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Czech description
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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
10100 - Mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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