A SYMMETRICAL PROPERTY OF THE SPECTRAL TRACE IN BANACH ALGEBRAS

Abstract. 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 Toit Mouton.