A Symmetrical Property of the Spectral Trace in Banach Algebras
Palabras clave:
Banach algebra, rank, spectral additivity, trace, subharmonic functionResumen
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.
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Referencias
B. Aupetit, “ A Primer on Spectral Theory ”, Universitext, Springer-Verlag, New York, 1991.
B. Aupetit, Trace and spectrum preserving linear mappings in Jordan-Banach algebras, Monatsh. Math. 125 (1998), 179 – 187.
B. Aupetit, H. du T. Mouton, Trace and Determinant in Banach algebras, Studia Math. 121 (2) (1996), 115 – 136.
G. Braatvedt, R. Brits, F. Schultz, Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems, Studia Math. 229 (2015), 173 – 180.
M. Kennedy, H. Radjavi, Spectral conditions on Lie and Jordan algebras of compact operators, J. Funct. Anal. 256 (2009), 3143 – 3157.
