A Short Proof that $M_{n}(A)$ is local if $A$ is local and Fr\'echet
funct-an
2016-02-12 v1 Operator Algebras
Abstract
We give a short and very general proof of the fact that the property of a dense Fr\'echet subalgebra of a Banach algebra being local, or closed under the holomorphic functional calculus in the Banach algebra, is preserved by tensoring with the matrix algebra of the complex numbers.
Keywords
Cite
@article{arxiv.funct-an/9211005,
title = {A Short Proof that $M_{n}(A)$ is local if $A$ is local and Fr\'echet},
author = {Larry B. Schweitzer},
journal= {arXiv preprint arXiv:funct-an/9211005},
year = {2016}
}
Comments
12 pages, plain Tex version 2.95