A $C^*$-algebra of entire functions
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- by Pan Ma and Kehe Zhu;
- Proc. Amer. Math. Soc. 152 (2024), 2131-2144
- DOI: https://doi.org/10.1090/proc/16711
- Published electronically: March 14, 2024
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Abstract:
We study the maximal abelian von Neumann algebra corresponding to $L^\infty (\mathbb {R})$ via the Bargmann transform. It is naturally an algebra of operators on the Fock space $F^2$, but it can also be realized as a function algebra contained in $F^2$. This provides an interesting example of a $C^*$ algebra whose elements are analytic functions.References
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Bibliographic Information
- Pan Ma
- Affiliation: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People’s Republic of China
- MR Author ID: 1156539
- Email: pan.ma@csu.edu.cn
- Kehe Zhu
- Affiliation: Department of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222
- MR Author ID: 187055
- Email: kzhu@albany.edu
- Received by editor(s): August 12, 2023
- Received by editor(s) in revised form: October 18, 2023
- Published electronically: March 14, 2024
- Additional Notes: The first author was supported by NNSF of China (Grant numbers 11801572 and 12171484), the Natural Science Foundation of Hunan Province (Grant number 2023JJ20056), the Science and Technology Innovation Program of Hunan Province (Grant number 2023RC3028), and Central South University Innovation-Driven Research Programme (Grant number 2023CXQD032). The second author was partially supported by NNSF of China (Grant number 12271328).
- Communicated by: Javad Mashreghi
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 2131-2144
- MSC (2020): Primary 30H20, 46J15, 47G10
- DOI: https://doi.org/10.1090/proc/16711
- MathSciNet review: 4728478