🚀 go-pugleaf

Hello All,

I need help proving an addition to the spectral mapping theorem:

Given:
1)   (X,||x||) is a Banach space 
2)   A is a bounded linear  operator on X (possibly of infinite 
dimension)
      A is not necessarily continuous
3)   0 is a regular value of the resolvent of A
4)   s(A) is the spectrum of A

Prove that:  

s(A^[-1])=s(A)^(-1)

Where s(A)^(-1) is the set {x^(-1)|x is an element of s(A)}

I�m kind of stuck,  so I would greatly appreciate any clues.

Frank