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

Larry B. Schweitzer

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

Larry B. Schweitzer

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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.

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BibTeX RIS

Larry B. Schweitzer. 1992-11-25. A Short Proof that $M_{n}(A)$ is local if $A$ is local and Fréchet. https://arxiv.org/abs/funct-an/9211005

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