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Properties of Linear Relations in Banach Spaces

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, Shandong, People’s Republic of China

    Guojing Ren

  2. Department of Mathematics, Texas AM University-Kingsville, Kingsville, TX, 78363, USA

    Ravi P. Agarwal

Authors
  1. Guojing Ren
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  2. Ravi P. Agarwal
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Correspondence to Guojing Ren.

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Communicated by Sanne ter Horst, Dmitry Kaliuzhnyi-Verbovetskyi and Izchak Lewkowicz.

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This work was supported by the National Natural Science Foundation of China (Grant Numbers 11301304, 11425105, 11571202) and General Financial Grant from the China Postdoctoral Science Foundation (Grant Number 2015M582069).

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Ren, G., Agarwal, R.P. Properties of Linear Relations in Banach Spaces. Complex Anal. Oper. Theory 13, 1917–1930 (2019). https://doi.org/10.1007/s11785-018-0876-4

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  • DOI: https://doi.org/10.1007/s11785-018-0876-4

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