A generalization of multiplicatively absorbing algebras (Q2765276)

A new class of topological algebras -- multiplicatively quasi absorbing algebras -- is introduced and its properties are studied. A topological algebra \(A\) is multiplicatively quasi absorbing if for each neighbourhood \(U\) of zero in \(A\) there is a neighbourhood of zero \(V\) such that for each \(a\in A\) there is a constant \(C=C_{a,U,V}\) with \(aV\subset CU\) and \(Va\subset CU\). It is easy to see that every topological algebra (with jointly continuous multiplication) is multiplicatively quasi absorbing and every multiplicatively quasi absorbing algebra is a topological algebra with separately continuous multiplication (a semitopological algebra in the author's terminology). The cases when the underlying linear topological space of \(A\) is locally convex and locally pseudoconvex are considered separately. An example of a topological algebra (with separately continuous multiplication) which is not multiplicatively quasi absorbing is given.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00059].