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The pseudospectra of bounded linear operators on quasi normed space

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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.

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.

참고문헌 (11)

  1. A. Ammar, "Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω", Filomat, 33(12), pp.3961~3975 (2019)
  2. A. Ammar, "The ε-pseudospectra and the essential ε-pseudospectra of linear relations", J. Pseudo-Differ. Oper. Appl, 11(2), pp.879~915 (2020)[DOI]
  3. A. Ammar, "Pseudo S-spectrum in a right quaternionic Hilbert space", Linear Multilinear Algebra, 70(4), pp.581~605 (2022)[DOI]
  4. E. B. Davies, "Linear operators and their spectra, Cambridge Studies in Advanced Mathematics, 106" (2007), Cambridge Univ. Press
  5. A. M. Pavlovic, "Quasi-Banach spaces. Function Classes on the Unit Disc: An Introduction" (2019), De Gruyter
  6. G. Rano, "Hahn-Banach extension theorem in quasi normed linear spaces", Advances in Fuzzy Mathematics (AFM), 12(4), pp.825~833 (2017)
  7. G. Rano, "Bounded linear operators in quasi-normed linear space", J. Egyptian Math. Soc, 23(2), pp.303~308 (2015)[DOI]
  8. L. N. Trefethen, "Spectra and Pseudospectra. The Behavior of Nonnormal Matrices and Operators" (2005), Princeton University Press
  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(2), pp.229~244 (2001)[DOI]
  11. C. Wu, "On the triangle inequality in quasi-Banach spaces", JIPAM. J. Inequal. Pure Appl. Math, 9(2), pp.41~45 (2008)[DOI]

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