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Does the Banach algebra of jets have the approximation property?
To formulate my question I need the construction of the algebra $J^n_M(K)$ of jets of degree $n$ on a compact set $K$ of a smooth manifold $M$. … Let us call its closure the algebra of jets of degree 1 of smooth functions on $\mathbb R$ on the subset $[0,1]$ and denote it by
$$
J^1_{\mathbb R}[0,1]=\overline{\varphi(C^\infty(\mathbb R))}
$$
Being …