Spectral Radius

Abstract

If λ₀ is not in the spectrum of A and if |λ — λ ₀| is sufficiently small, then

$$ {\rho _A}(\lambda ){\kern 1pt} = {\left( {A\, - \,{\lambda _0}} \right)^{ - 1}}\;\sum\limits_{n = 0}^\infty {{{({{(A\, - \,{\lambda _0})}^{ - 1}}(\lambda \, - \,{\lambda _0}))}^n}} $$