Properties of Linear Relations in Banach Spaces
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This paper is concerned with properties and stability of linear relations, including closed, compact, and Fredholm linear relations. Stability of closedness and compactness of linear relations under relatively bounded perturbations and relatively compact perturbations is studied. In particular, results on the stability of index of Fredholm linear relation and its iterates are discussed. The results obtained in the present paper generalize the corresponding results for single-valued linear operators to multi-valued linear operators, and some improve or relax certain assumptions of the related existing results.
KeywordsLinear relation Perturbation Closedness Compactness Fredholm
Mathematics Subject Classification47A06 47A53 47A55
- 8.Coddington, E.A.: Extension theory of formally normal and symmetric linear relations. Mem. Am. Math. Soc. 134 (1973)Google Scholar
- 17.Ren, G.: Stability of index for linear relations and its applications. Indagationes Mathematicae (2017), In PressGoogle Scholar