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For $m>0$ we consider the ring $C^{\infty}(\mathbb{R}^{m})$ of smooth functions on $\mathbb{R}^{m}$. For $n>0$ we consider the projection $\mathbb{R}^{m+n}\to \mathbb{R}^{m}$ hence $C^{\infty}(\mathbb …

Let $A$ be a nuclear Frechet algebra with unit. Let $M$ be a right Frechet $A$-module and $N$ be a left Frechet $A$-module. Both $M$ and $N$ are assumed to be non-degenerate. We can define the project …

Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection of semi-norm defined by $p_{\alpha}(f):=\sup_{\beta\leq\ …

The question is a special case of a previous question. Let $M$ be a compact smooth manifold, then it is clear that $C^{\infty}(M)$ is a Frechet algebra with pointwise multiplication and a collection …