We prove that if a semisimple real or complex Banach algebra A possesses an algebraic derivation whose invariants are algebraic, then A is finite-dimensional. This result is a full generalization of a recent result by Haily, Kaidi and Palacios (2011)  for the case of inner derivations in complex semisimple Banach algebras. The analogous result for automorphism case is also obtained.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory