Fock structure of complete Boolean algebras of type I factors and of unital factorizations

Vidmar, Matija (author)

The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En route, the spectral theory of noise-type Boolean algebras of Tsirelson is cast in the noncommutative language of “factorizations with unit” for which a multi-layered characterization of being “of Fock type” is provided.

• Language: English
• Keywords: factorization, completeness, Fock space, spectrum, independence, Boolean algebra
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 35 str.
• Numbering: Vol. 542, iss. 1, art. 128780
• PID: 20.500.12556/RUL-160516
• UDC: 519.2
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2024.128780
• COBISS.SI-ID: 205623811
• Publication date in RUL: 29.08.2024

Record is a part of a journal

• Title: Journal of mathematical analysis and applications
• Shortened title: J. math. anal. appl.
• Publisher: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: faktorizacija, faktor tipa I, polnost, Fockov prostor, produktni vektor, komutativna von Neumannova algebra, spekter, neodvisnost, stohastični šum, šumna Boolova algebra

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0402
• Name: Matematična fizika

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P1-0448
• Name: Stohastične metode in njihova uporaba