Spectral theory for non-associative complete normed algebras and automatic continuity

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 Higher Derivations on JB*-Algebras

automatic continuity of homomorphisms between banach algebras and frechet algebras

Automatic Continuity in Associative and Nonassociative Context

There are excellent accounts on automatic continuity theory in the associative context. Since there have been a number of advances in automatic continuity theory in the nonassociative context, it seems to be an opportune time to present a comprehensive discussion of the currently known results on automatic continuity of linear maps in this context. These notes are an attempt to collect together...