Unital strongly harmonic commutative Banach algebras

Abstract

A unital commutative Banach algebra ${\cal A}$ is spectrally separable if for any two distinct non-zero multiplicative linear functionals $ \varphi $ and $ \psi $ on it there exist $ a $ and $ b $ in $ {\cal A}$ such that $ ab=0 $ and $ \varphi (a)\psi (b