Multipliers in perfect locally \(m\)-convex algebras (Q2341412)

Let \(A\) be a locally \(m\)-convex algebra and \(\{p_\lambda:\lambda\in\Lambda\}\) the collection of seminorms which defines the topology of \(A\). For every \(\lambda\in\Lambda\), let \(A_\lambda=A\ker p_\lambda\). In the case when every projection \(\pi _\lambda\) : from \(\prod _{\lambda\in\Lambda} A_\lambda\) to \(A_\lambda\) is surjective, \(A\) is called perfect. The following is proved: if \(A\) is a complete and perfect locally \(m\)-convex algebra for which every factor algebra \(A_\lambda\) is complete, then the multiplier algebra \(M(A)\) of \(A\) is topologically isomorphic to the projective limit of multiplier algebras \(M(A_\lambda) \) of \(A_\lambda\).