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Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems

Volume 229 / 2015

Gareth Braatvedt, Rudolf Brits, Francois Schulz Studia Mathematica 229 (2015), 173-180 MSC: Primary 46H05, 46H10; Secondary 15A45. DOI: 10.4064/sm8157-12-2015 Published online: 3 December 2015

Abstract

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.

Authors

  • Gareth BraatvedtDepartment of Pure and Applied Mathematics
    University of Johannesburg
    Johannesburg, South Africa
    e-mail
  • Rudolf BritsDepartment of Pure and Applied Mathematics
    University of Johannesburg
    Johannesburg, South Africa
    e-mail
  • Francois SchulzDepartment of Pure and Applied Mathematics
    University of Johannesburg
    Johannesburg, South Africa
    e-mail

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