Publication Type : Journal Article
Publisher : Springer Science and Business Media LLC
Source : Complex Analysis and Operator Theory
Url : https://doi.org/10.1007/s11785-024-01506-4
Campus : Haridwar
School : School of Engineering
Department : Mathematics
Year : 2024
Abstract : In this short note, the second dual of generalized group algebra (ℓ1(𝐺,𝐴),∗) equipped with both Arens product is investigated, where G is any discrete group and 𝐴 is a Banach algebra containing a complemented algebraic copy of (ℓ1(𝑁),∙) . We give an explicit family of annihilators(w.r.t both the Arens product) in the algebra ℓ1(𝐺,𝐴)∗∗ , arising from non-principal ultrafilters on 𝑁 and which are not in the toplogical center. As a consequence, we also deduce the fact that ℓ1(𝐺,𝐴) is not Strongly Arens irregular.
Cite this Research Publication : Lav Kumar Singh, Annihilators in the Bidual of the Generalized Group Algebra of a Discrete Group, Complex Analysis and Operator Theory, Springer Science and Business Media LLC, 2024, https://doi.org/10.1007/s11785-024-01506-4