Spectral rank of maximal finite-rank elements in Banach-Jordan algebras

We give a new proof to a spectral characterisation of the spectral rank established by Aupetit by replacing his deep analytic arguments by the new characterisation of the connected component of the group of invertible elements obtained by O. Loos.peerReviewe

Spectral rank of maximal finite-rank elements in Banach-Jordan algebras

We give a new proof to a spectral characterisation of the spectral rank established by Aupetit by replacing his deep analytic arguments by the new characterisation of the connected component of the group of invertible elements obtained by O. Loos.peerReviewe

A symmetrical property of the spectral trace in Banach algebras

Our aim in this paper is to extend a symmetrical property of the trace by M. Kennedy and H. Radjavi for bounded operators on a Banach space to the more general situation of Banach algebras. The main ingredients are Vesentini's result on subharmonicity of the spectral radius and the new spectral rank and trace defined on the socle of a Banach algebra by B. Aupetit and H. du T. Mouton.peerReviewe

Linear codes with arbitrary dimensional hull and pure LCD code

In this paper, we introduce a general construction of linear codes with small dimension hull from any non LCD codes. Furthermore, we show that for any linear code \Co over \F_q ($q > 3$) with dim(Hull(\Co))=h there exist an equivalent codes \Co_j with dim(Hull(\Co_j))=j for any integer $0\leq j \leq h$. We also introduce the notion of pure LCD code; an LCD code and all its equivalent are LCD; and construct an infinite family of pure LCD codes. In addition, we introduce a general construction of linear codes with one dimension hull