Embedding of a separable locally pseudoconvex algebra into a locally pseudoconvex algebra with two generators (Q1201230)

Let \(0<p\leq 1\). A \(p\)-homogeneous semi-norm on a vector space \(X\) is a non-negative real function on \(X\) such that \(p(x+y)\leq p(x)+p(y)\) and \(p(\lambda x)=|\lambda|^ p p(x)\) for \(x,y\in E\) and \(\lambda\in\mathbb{R}\). A locally pseudo-convex space is a topological vector space whose topology is defined by a system of \(p(\alpha)\)-homogeneous semi-norms \((0<p(\alpha)\leq 1)\). These spaces generalize both locally convex and locally bounded spaces. A locally pseudo-convex algebra is an algebra which is a locally pseudo convex space with a multiplication jointly continuous. The main result of this paper is the following: Let \(A\) be a separable and complete locally pseudo convex algebra on \(\mathbb{K}=\mathbb{R}\) or \(\mathbb{C}\). There exists a unital locally pseudo-convex algebra \(B\), topologically generated by two elements and an isomorphism \(F: A\to B\).