On the regularity of homomorphisms between Riesz subalgebras of \(\mathcal{L}^r(X)\) (Q904174)

The paper deals with the automatic regularity of different maps. In Part 3, some sufficient conditions for a sequentially continuous algebra homomorphism between topological algebras (with separately continuous multiplication) to be regular are given. In Part 4, the similar problem is considered for continuous algebra homomorphisms between normed (operator) algebras or Riesz (operator) algebras or their ideals, where the operators are defined on certain Banach lattices. The last section deals with the automorphisms of an algebra of operators on a reflexive purely atomic Banach lattice. Reviewer's remark: It is very much appreciated that the author considers a topological algebra to be an algebra with separately continuous multiplication instead of a jointly continuous multiplication. Jointly continuous multiplication is very often a too strict demand, which can be replaced by the separate continuity of the multiplication.