Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the structure of ideals and multipliers: A unified approach


Authors: Mostafa Mbekhta and Matthias Neufang
Journal: Proc. Amer. Math. Soc. 147 (2019), 4757-4769
MSC (2010): Primary 43A10, 43A20, 46H10
DOI: https://doi.org/10.1090/proc/14676
Published electronically: August 7, 2019
MathSciNet review: 4011510
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the structure of one-sided ideals in a Banach algebra $\mathcal {A}$. We find very general conditions under which any left (right) ideal is of the form $\mathcal {A} q$ ($q \mathcal {A}$) for some idempotent right (left) multiplier on $\mathcal {A}$. We further show that a large class of one-sided multipliers can be realized as a product of an invertible and an idempotent multiplier. Applying our results to algebras over locally compact quantum groups and $C^*$-algebras, we demonstrate that our approach generalizes and unifies various theorems from abstract harmonic analysis and operator algebra theory. In particular, we generalize results of Bekka (and Reiter), Berglund, Forrest, and Lau–Losert. We also deduce the Choquet–Deny theorem for compact groups as an application of our approach. Moreover, we answer, for a certain class of measures on a compact group, a question of Ülger which, in the abelian case, goes back to Beurling (1938).


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 43A10, 43A20, 46H10

Retrieve articles in all journals with MSC (2010): 43A10, 43A20, 46H10


Additional Information

Mostafa Mbekhta
Affiliation: Laboratoire de Mathématiques Paul Painlevé (UMR CNRS 8524), Université de Lille, Département de Mathématiques, 59655 Villeneuve d’Ascq Cedex, France
MR Author ID: 121980
Email: mostafa.mbekhta@univ-lille.fr

Matthias Neufang
Affiliation: School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada; and Laboratoire de Mathématiques Paul Painlevé (UMR CNRS 8524), Université de Lille, Département de Mathématiques, 59655 Villeneuve d’Ascq Cedex, France
MR Author ID: 718390
Email: mneufang@math.carleton.ca; matthias.neufang@univ-lille.fr

Received by editor(s): January 2, 2019
Published electronically: August 7, 2019
Additional Notes: This work was supported in part by the Labex CEMPI (ANR-11-LABX-0007-01). The second author was partially supported by NSERC Discovery Grant RGPIN-2014-06356. This support is gratefully acknowledged.
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2019 American Mathematical Society