Characterizations of a commutative semisimple modular annihilator Banach algebra through its socle




Commutative algebras, Socle, Inessential element, Completely continuous algebra, Modular annihilator algebra


Let A be a commutative complex semisimple Banach algebra. In this paper we continue the study of kh(soc(A)). Thus we will give, among other things, some new characterizations of this ideal in terms of the closure, in the spectral radius norm, of the socle of A.

Author Biographies

Youness Hadder, Sidi Mohamed Ben Abdellah University Atlas

Laboratoire de Sciences Math´ematiques et Applications (LaSMA).

Dhar El Mahraz Faculty of Sciences.

Abdelkhalek El Amrani, Sidi Mohamed Ben Abdellah University

Departement de Mathematiques, Faculte des Sciences Dhar-Mehraz


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How to Cite

Y. Hadder and A. El Amrani, “Characterizations of a commutative semisimple modular annihilator Banach algebra through its socle”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 697-709, May 2021.




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