On invertibility preserving linear maps, simultaneous triangularization and Property L
funct-an
2008-02-03 v1 Operator Algebras
Abstract
Let F be a linear unital map of a unital matrix algebra A over the complex numbers into the complex n by n matrices. Then F induces a linear unital map Fk of the k by k matrices over A into the complex nk by nk matrices by the action of F on each entry in the k by k matrices. If Fk preserves invertibility and k is greater than dim(alg(F(A)))-dim(F(A))+2 then F is a homomorphism modulo the Jacobson radical in alg(F(A)). The paper also contains some results related to the property L and some sufficient conditions for simultaneous triangularization of sets of matrices.
Keywords
Cite
@article{arxiv.funct-an/9702017,
title = {On invertibility preserving linear maps, simultaneous triangularization and Property L},
author = {Erik Christensen},
journal= {arXiv preprint arXiv:funct-an/9702017},
year = {2008}
}
Comments
amstex, 18 pages