A SHORT PROOF THAT M<sub>n</sub>(A) IS LOCAL IF A IS LOCAL AND FRÉCHET
A SHORT PROOF THAT M<sub>n</sub>(A) IS LOCAL IF A IS LOCAL AND FRÉCHET
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 m the Banach algebra, is preserved by tensoring with the n×n matnx algebra of the complex numbers