Decomposition of spectrum

Question

We know that if X is a banach space and T be an element in Banach Algebra B(X) then the union of residual spectrum continuous spectrum and point spectrum is spectrum of Banach algebra i.e σ(T) is the disjoint union of these three sets,i.e $\sigma (T)=\sigma _{p}(T)\cup \sigma _{c}(T)\cup \sigma _{r}(T)$ for T in Banach Algebra But I have no idea how to prove this disjoint decomposition.