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Regular linear relations on Banach spaces

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Abstract

For a Banach space, the notion of a regular linear relation is introduced and studied. Also, the regular resolvent set for a closed linear relation is introduced and investigated. Certain characterizations of regular resolvents are obtained in terms of the gap metric between corresponding null spaces, and in terms of generalized resolvents of the linear relation itself, respectively.

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Acknowledgements

The authors would like to thank the reviewer for his/her thoughtful comments and efforts towards improving the present paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Oviedo, 33007, Oviedo, Asturias, Spain

    Teresa Alvarez

  2. Department of Mathematics, “Gheorghe Asachi” Technical University, B-dul Carol I nr. 11, 700506, Iaşi, Romania

    Adrian Sandovici

Authors
  1. Teresa Alvarez
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  2. Adrian Sandovici
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Correspondence to Adrian Sandovici.

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Communicated by Raul Curto.

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Alvarez, T., Sandovici, A. Regular linear relations on Banach spaces. Banach J. Math. Anal. 15, 4 (2021). https://doi.org/10.1007/s43037-020-00092-9

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  • DOI: https://doi.org/10.1007/s43037-020-00092-9

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