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

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

1992-11-25

arxiv.org/abs/funct-an/9211005v1

Mathematics

Operator Algebras

12 pages, plain Tex version 2.95

Scientific paper

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 $n\times n$ matrix algebra of the complex numbers.

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