Spectral Theory For Strongly Continuous Cosine

Abstract

Abstract Let (C(t))t∈ℝ be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – cosh λt is semi-Fredholm (resp. semi-Browder, Drazin inversible, left essentially Drazin and right essentially Drazin invertible) operator and λt ∉ iπℤ, then A – λ2 is also. We show by counterexample that the converse is false in general.