- Problem 9. Let R, = (A - N) and R₁ = (A - μl)¹ be the resolvents corresponding to the points λ and μ. Prove that RR₁ = RR, and RR = (-1)RRx. Hint. Multiply both sides of (19) by (A)(A - µI). (19) Comment. It follows from (19) that if λo is a regular point of A, then the derivative of R, with respect to λ at the point λo, i.e., the limit lim Ro+A-Ro 4X40 Δλ λο (in the sense of convergence with respect to the operator norm) exists and equals R ning a complex