Journal article
The degree one Laguerre-Pólya class and the shuffle-word-embedding conjecture
Canadian mathematical bulletin
28 Feb 2024
Abstract
We discuss the class of functions, which are well approximated on compacta by the geometric mean of the eigenvalues of a unital (completely) positive map into a matrix algebra or more generally a type $II_1$ factor, using the notion of a Fuglede-Kadison determinant. In two variables, the two classes are the same, but in three or more noncommuting variables, there are generally functions arising from type $II_1$ von Neumann algebras, due to the recently established failure of the Connes embedding conjecture. The question of whether or not approximability holds for scalar inputs is shown to be equivalent to a restricted form of the Connes embedding conjecture, the so-called shuffle-word-embedding conjecture.
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Details
- Title
- The degree one Laguerre-Pólya class and the shuffle-word-embedding conjecture
- Creators
- James E. Pascoe - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- Canadian mathematical bulletin
- Publisher
- Cambridge Univ Press
- Number of pages
- 8
- Grant note
- DMS 2319010; DMS 2000037 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001192268200001
- Scopus ID
- 2-s2.0-85186892612
- Other Identifier
- 991021879629304721
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- Mathematics