The center of primitive locally pseudoconvex algebras (Q1772519)

Let \(A\) be a topological algebra over the real or complex field. For each \(a \in A\) and each maximal regular left ideal \(M\) of \(A\), let \(L_a^M\) be a mapping of \(A/M\) into itself which takes \(x \in A/M\) into \(ax\). Let \(L_M\) be the mapping of \(A\) into the space of all endomorphisms on \(A/M\) defined by \(L_M(a) = L_a^M\) for each \(a \in A\). Then a topological algebra \(A\) is called a primitive algebra if it contains a maximal regular left (or right) ideal \(M\) such that the kernel of \(L_M\) is zero, and is called a topologically primitive algebra if this ideal \(M\) is closed. With these definitions, it is shown that the center of a unital primitive \(A\)-pseudoconvex Hausdorff algebra over the complex numbers and of a unital topologically primitive locally pseudoconvex Fréchet algebra over the complex numbers are topologically isomorphic to the space of complex numbers.