English

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 n×nn\times n 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