The aim of this article is to study a number of relationship between Frechet algebra $\mathcal{ A}$ and its ultrapower $(\mathcal{ A})_{ \mathcal{ U}}$. We give a characterization in some aspects such as locally bounded approximate identity. We consider the notion of contractibility of ultrapower of Frechet algebra, and we show that if $(\mathcal{ A})_{ \mathcal{ U}}$ has approximation property with good ultrafilter $\mathcal{ U}$ then $\mathcal{ A}$ is contractible if and only if $(\mathcal{ A})_{ \mathcal{ U}}$ is contractible.
Categories: math.FA