The continuity of Lie homomorphisms
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
The Gleason-Kahane-Żelazko theorem and its generalizations
This expository article deals with results surrounding the following question: Which pairs of Banach algebras A and B have the property that every unital invertibility preserving linear map from A to B is a Jordan homomorphism?
The spectrally bounded linear maps on operator algebras
We show that every spectrally bounded linear map Φ from a Banach algebra onto a standard operator algebra acting on a complex Banach space is square-zero preserving. This result is used to show that if Φ₂ is spectrally bounded, then Φ is a homomorphism multiplied by a nonzero complex number. As another application to the Hilbert space case, a classification theorem is obtained which states that every spectrally bounded linear bijection Φ from ℬ(H) onto ℬ(K), where H and K are infinite-dimensional...
Towards a non-selfadjoint version of Kadison's theorem.