Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
Gareth Braatvedt ; Rudolf Brits ; Francois Schulz
Studia Mathematica, Tome 231 (2015), p. 173-180 / Harvested from The Polish Digital Mathematics Library
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As a follow-up to a paper of Aupetit and Mouton (1996), we consider the spectral definitions of rank, trace and determinant applied to elements in a general Banach algebra. We prove a generalization of Sylvester's Determinant Theorem to Banach algebras and thereafter a generalization of the Frobenius inequality.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:285571 
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     year = {2015},
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Gareth Braatvedt; Rudolf Brits; Francois Schulz. Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems. Studia Mathematica, Tome 231 (2015) pp. 173-180. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8157-12-2015/