Les endomorphismes d'algèbre à poids
Local algebras and the largest spectrum finite ideal.
M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of...
Locally convex inductive limits of normed algebras
Locally m-pseudoconvex topologies on locally A-pseudoconvex algebras
Let be a locally A-pseudoconvex algebra over or . We define a new topology on which is the weakest among all m-pseudoconvex topologies on stronger than . We describe a family of non-homogeneous seminorms on which defines the topology .