Projective Spectrum in Banach Algebras

Consider a Banach algebra \({\mathcal B}\) with unit I. The classical spectrum of an element \(A\in {\mathcal B}\) is the set \(\sigma (A)=\{\lambda \in {\mathbb C} \mid \ A-\lambda I\ \text{is not invertible in }{\mathcal B}\}\) , and it is one of the main subjects in operator theory.