Strong continuity of semigroup homomorphisms

Automatic continuity of group homomorphisms

We survey various aspects of the problem of automatic continuity of homomorphisms between Polish groups.

Continuity of Homomorphisms on Pro-nilpotent Algebras

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras Ai ∈V, such that some finitely generated subalgebra S ⊆A is dense in A under the inverse limit of the discrete topologies on the Ai. A sufficient condition on V is obtained for all algebra homomorphisms from A to finite-dimensional algebras B to be continuous; in other words, for the kernels...

Automatic continuity of surjective $n$-homomorphisms on Banach algebras

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

The Kernels and Continuity Ideals of Homomorphisms

We give a description of the continuity ideals and the kernels of homomorphisms from the algebras of continuous functions on locally compact spaces into Banach algebras.