Positive approximate identity in a Banach lattice algebra
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- by Youssef Azouzi and Jamel Jaber;
- Proc. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/proc/16801
- Published electronically: June 26, 2025
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Abstract:
Addressing an open problem, this paper provides a positive answer to whether a Banach lattice algebra with contractive approximate identities also possesses a positive one. Furthermore, we establish that the projective tensor product of Banach lattice algebras $A$ and $B$ has a positive approximate identity if and only if both $A$ and $B$ exhibit this property.References
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Bibliographic Information
- Youssef Azouzi
- Affiliation: Research Laboratory of Algebra, Topology, Arithmetic, and Order, Department of Mathematics, COSAEF, Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis-El Manar University, 2092-El Manar, Tunisia
- MR Author ID: 858092
- ORCID: 0000-0003-1560-5726
- Jamel Jaber
- Affiliation: Research Laboratory of Algebra, Topology, Arithmetic, and Order, Department of Mathematics, COSAEF, Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis-El Manar University, 2092-El Manar, Tunisia
- MR Author ID: 903422
- Received by editor(s): December 15, 2023
- Received by editor(s) in revised form: January 17, 2024, January 21, 2024, and January 26, 2024
- Published electronically: June 26, 2025
- Additional Notes: The authors are members of the GOSAEF research group
- Communicated by: Stephen Dilworth
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
- MSC (2020): Primary 97H50, 47A58
- DOI: https://doi.org/10.1090/proc/16801