Automatic Continuity of Dense Range Homomorphisms into Multiplicatively Semisimple Complete Normed Algebras

Continuity of homomorphisms into complete normed algebraic algebras

We prove that, if A and B are complete normed non-associative algebras, and if B is strongly semisimple and algebraic, then dense range homomorphisms from A to B are continuous. As a consequence, we obtain that homomorphisms from complete normed algebras into a complete normed power-associative algebraic algebra B are continuous if and only if B has no nonzero elements with zero square. We also...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

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

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.