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

Gareth Braatvedt, Rudolf Brits, and Francois Schulz. "Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems." Studia Mathematica 229.2 (2015): 173-180. <http://eudml.org/doc/285571>.

@article{GarethBraatvedt2015,
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.},
author = {Gareth Braatvedt, Rudolf Brits, Francois Schulz},
journal = {Studia Mathematica},
keywords = {Banach algebra; spectrum; socle; rank},
language = {eng},
number = {2},
pages = {173-180},
title = {Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems},
url = {http://eudml.org/doc/285571},
volume = {229},
year = {2015},
}

TY - JOUR
AU - Gareth Braatvedt
AU - Rudolf Brits
AU - Francois Schulz
TI - Rank, trace and determinant in Banach algebras: generalized Frobenius and Sylvester theorems
JO - Studia Mathematica
PY - 2015
VL - 229
IS - 2
SP - 173
EP - 180
AB - 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.
LA - eng
KW - Banach algebra; spectrum; socle; rank
UR - http://eudml.org/doc/285571
ER -