On the quasi-Fredholm and Saphar spectrum of strongly continuous Cosine operator function

Abstract

Let (C(t))t∈𝕉 be a strongly continuous cosine family and A be its infinitesimal generator. In this work, we prove that, if C(t) – coshλt is Saphar (resp. quasi-Fredholm) operator and λt /∉iπ𝕑, then A – λ2 is also Saphar (resp. quasi-Fredholm) operator. We show by counter-example that the converse is false in general.

Keywords

• cosine
• quasi-fredholm
• semi-regular
• saphar
• 47a10
• 47d62