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

Trace and determinant in Jordan-Banach algebras ALGEBRAS

Using an appropriate definition of the multiplicity of a spectral value, we introduce a new definition of the trace and determinant of elements with finite spectrum in Jordan-Banach algebras. We first extend a result obtained by J. Zemánek in the associative case, on the connectedness of projections which are close to each other spectrally (Theorem 2.3). Secondly we show that the rank of the Riesz projection associated to a finite-rank element a and a finite subset of its spectrum is equal to the sum of the multiplicities of these spectral values (Theorem 2.6). Then we turn to the study of properties such as linearity and continuity of the trace and multiplicativity of the determinant

High gain adaptive observer design for sensorless state and parameter estimation of induction motors

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