Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
Tom 229 / 2015
Studia Mathematica 229 (2015), 173-180 MSC: Primary 46H05, 46H10; Secondary 15A45. DOI: 10.4064/sm8157-12-2015 Opublikowany online: 3 December 2015
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.