Abstract
In this chapter the perturbation theory developed for bounded Fredholm operators in Sections XI.3 and XI.4 is extended to closed unbounded Fredholm operators. For the additive perturbation theorems this is accomplished via the simple device of renorming the domain of the operator T. In this way T becomes a bounded Fredholm operator to which the theorems of Chapter XI are applicable. We start with some properties and examples of the graph norm. The third and fourth section contain the main perturbation theorems. Section 5 presents a completeness theorem for certain compact perturbations of unbounded selfadjoint operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Basel AG
About this chapter
Cite this chapter
Gohberg, I., Goldberg, S., Kaashoek, M.A. (1990). Unbounded Fredholm Operators and Perturbation Theorems. In: Classes of Linear Operators Vol. I. Operator Theory: Advances and Applications, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7509-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7509-7_18
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7511-0
Online ISBN: 978-3-0348-7509-7
eBook Packages: Springer Book Archive