A Short Proof that $M_{n}(A)$ is local if $A$ is local and Fréchet

Larry B. Schweitzer

paper

A Short Proof that $M_{n} (A)$ is local if $A$ is local and Fréchet

arXiv:funct-an/9211005

Abstract

We give a short and very general proof of the fact that the property of a dense Fréchet subalgebra of a Banach algebra being local, or closed under the holomorphic functional calculus in the Banach algebra, is preserved by tensoring with the $n \times n$ matrix algebra of the complex numbers.

arXiv comment12 pages, plain Tex version 2.95

A Short Proof that Mn​(A) is local if A is local and Fréchet

Abstract

A Short Proof that $M_{n} (A)$ is local if $A$ is local and Fréchet