Revista de la
Unión Matemática Argentina
The reconstruction problem for a multivalued linear operator's properties
Nihel Feki and Maher Mnif

Volume 68, no. 1 (2025), pp. 145–162    

Published online (final version): April 11, 2025

https://doi.org/10.33044/revuma.3425

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Abstract

The reconstruction problem for a multivalued linear operator (linear relation) $T$ is viewed as the exploration of some properties of $T$ from those of a restriction of $T$ on an invariant linear subspace.

References

  1. T. Álvarez, On regular linear relations, Acta Math. Sin. (Engl. Ser.) 28 no. 1 (2012), 183–194.  DOI  MR  Zbl
  2. C.-G. Ambrozie and F.-H. Vasilescu, Banach space complexes, Mathematics and its Applications 334, Kluwer Academic Publishers, Dordrecht, 1995.  DOI  MR  Zbl
  3. R. Arens, Operational calculus of linear relations, Pacific J. Math. 11 (1961), 9–23.  MR  Zbl Available at http://projecteuclid.org/euclid.pjm/1103037531.
  4. B. A. Barnes, Restrictions of bounded linear operators: closed range, Proc. Amer. Math. Soc. 135 no. 6 (2007), 1735–1740.  DOI  MR  Zbl
  5. A. G. Baskakov and A. S. Zagorskiĭ, On the spectral theory of linear relations on real Banach spaces (in Russian), Mat. Zametki 81 no. 1 (2007), 17–31, English translation in Math. Notes 81 no. 1 (2007), 15–27.  DOI  MR  Zbl
  6. E. Chafai and M. Mnif, Ascent and essential ascent spectrum of linear relations, Extracta Math. 31 no. 2 (2016), 145–167.  MR  Zbl
  7. R. Cross, Multivalued linear operators, Monographs and Textbooks in Pure and Applied Mathematics 213, Marcel Dekker, New York, 1998.  MR  Zbl
  8. J. Dixmier, Étude sur les variétés et les opérateurs de Julia, avec quelques applications, Bull. Soc. Math. France 77 (1949), 11–101.  DOI  MR  Zbl
  9. S. V. Djordjević and B. P. Duggal, Spectral properties of linear operator through invariant subspaces, Funct. Anal. Approx. Comput. 1 no. 1 (2009), 19–29.  MR  Zbl
  10. S. V. Djordjević and B. P. Duggal, Drazin invertibility of the diagonal of an operator, Linear Multilinear Algebra 60 no. 1 (2012), 65–71.  DOI  MR  Zbl
  11. C. Foiaş, Invariant para-closed subspaces, Indiana Univ. Math. J. 20 no. 10 (1971), 897–900.  DOI  MR  Zbl
  12. A. Ghorbel and M. Mnif, Drazin inverse of multivalued operators and its applications, Monatsh. Math. 189 no. 2 (2019), 273–293.  DOI  MR  Zbl
  13. I. Issaoui and M. Mnif, Characterization of Saphar linear relations, Complex Anal. Oper. Theory 13 no. 8 (2019), 3753–3766.  DOI  MR  Zbl
  14. M. Lajnef and M. Mnif, On generalized Drazin invertible linear relations, Rocky Mountain J. Math. 50 no. 4 (2020), 1387–1408.  DOI  MR  Zbl
  15. P. Saveliev, Lomonosov's invariant subspace theorem for multivalued linear operators, Proc. Amer. Math. Soc. 131 no. 3 (2003), 825–834.  DOI  MR  Zbl
  16. A. E. Taylor and D. C. Lay, Introduction to functional analysis, second ed., John Wiley & Sons, New York, 1980.  MR  Zbl