Criteria of existence of bounded approximate identities in topological algebras (Q617788)

Some results known for Banach algebras are generalized to the general topological algebra setting or to the hypotopological algebra setting. Criteria for a topological algebra to have a left approximate identity are proven. Criteria for a right hypotopological algebra to possess left bounded approximate units are given. Some properties concerning ideals of a topological algebra, having bounded approximate identities, are considered. It is proved that a quasinormable Fréchet \(m\)-convex algebra \(A\) has a left bounded approximate identity if and only if it has an Arens-Michael reperesentation \(A=\varprojlim A_n\), where each \(A_n\) has a left bounded approximate identity.