Spectral isometries onto algebras having a separating family of   finite-dimensional irreducible representations
  We prove that if $\mathcal{A}$ is a complex, unital semisimple Banach algebra and $\mathcal{B}$ is a complex, unital Banach algebra having a separating family of finite-dimensional irreducible representations, then any unital linear operator from $\mathcal{A}$ onto $\mathcal{B}$ which preserves the spectral radius is a Jordan morphism. 
Constantin Costara, Du\v{s}an Repov\v{s}
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