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THE PSEUDOSPECTRA OF BOUNDED LINEAR OPERATORS ON QUASI NORMED SPACE

  • Aymen Ammar (Department of Mathematics Faculty of Sciences of Sfax University of Sfax) ;
  • Ameni Bouchekoua (Department of Mathematics Faculty of Sciences of Sfax University of Sfax) ;
  • Nawrez Lazrag (Department of Mathematics Faculty of Sciences of Sfax University of Sfax)
  • Received : 2022.05.28
  • Accepted : 2023.03.16
  • Published : 2023.07.31

Abstract

In this paper, we introduce the pseudospectra of bounded linear operators on quasi normed space and study its proprieties. Beside that, we establish the relationship between the pseudospectra of a sequence of bounded linear operators and its limit.

Keywords

References

  1. A. Ammar, A. Bouchekoua, and A. Jeribi, Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in 𝔼ω, Filomat 33 (2019), no. 12, 3961-3975.  https://doi.org/10.2298/FIL1912961A
  2. A. Ammar, A. Bouchekoua, and A. Jeribi, The ε-pseudospectra and the essential ε-pseudospectra of linear relations, J. Pseudo-Differ. Oper. Appl. 11 (2020), no. 2, 879-915. https://doi.org/10.1007/s11868-019-00300-7 
  3. A. Ammar, A. Jeribi, and N. Lazrag, Pseudo S-spectrum in a right quaternionic Hilbert space, Linear Multilinear Algebra 70 (2022), no. 4, 581-605. https://doi.org/10.1080/03081087.2020.1737632 
  4. E. B. Davies, Linear operators and their spectra, Cambridge Studies in Advanced Mathematics, 106, Cambridge Univ. Press, Cambridge, 2007. https://doi.org/10.1017/CBO9780511618864 
  5. A. M. Pavlovic, Quasi-Banach spaces. Function Classes on the Unit Disc: An Introduction, Berlin, Boston, De Gruyter, 2019. 
  6. G. Rano, Hahn-Banach extension theorem in quasi normed linear spaces, Advances in Fuzzy Mathematics (AFM) 12 (2017), no 4, 825-833. 
  7. G. Rano and T. Bag, Bounded linear operators in quasi-normed linear space, J. Egyptian Math. Soc. 23 (2015), no. 2, 303-308. https://doi.org/10.1016/j.joems.2014.06.003 
  8. L. N. Trefethen and M. Embree, Spectra and Pseudospectra. The Behavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, NJ, 2005. 
  9. J. M. Varah, The computaion of bounds for the invariant subspaces of a general matrix operator, 1975. 
  10. M. P. H. Wolff, Discrete approximation of unbounded operators and approximation of their spectra, J. Approx. Theory 113 (2001), no. 2, 229-244. https://doi.org/10.1006/jath.2001.3588 
  11. C. Wu and Y. J. Li, On the triangle inequality in quasi-Banach spaces, JIPAM. J. Inequal. Pure Appl. Math. 9 (2008), no. 2, Article 41, 4 pp.