Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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DIVISIBLE SUBSPACES OF LINEAR OPERATORS ON BANACH SPACES

  • Hyuk Han (Division of Liberal Arts Kongju National University)
  • Received : 2024.01.09
  • Accepted : 2024.01.29
  • Published : 2024.02.29
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Abstract

In this paper, we investigate the properties related to algebraic spectral subspaces and divisible subspaces of linear operators on a Banach space. In addition, using the concept of topological divisior of zero of a Banach algebra, we prove that the only closed divisible subspace of a bounded linear operator on a Banach space is trivial. We also give an example of a bounded linear operator on a Banach space with non-trivial divisible subspaces.

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References

  1. P. Aiena, Freholm and Local Spectral Theory, with Application to Multipliers, Kluwer Academic Publishers, Dordrecht, 2004.
  2. P. Aiena, Fredholm and Local Spectral Theory II, with Application to Weyl-type Theorems, Springer Nature Switzerland AG, 2018.
  3. B. Aupetit, A Primer on Spectral Theory, Spring-Verlag, New York, 1991.
  4. F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, 1973.
  5. I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
  6. H. G. Dales, Banach Algebras and Automatic Continuity, Oxford Science Publications, London Mathematical Society Monographs New Series 24, 2000.
  7. H. G. Dales, P. Aiena, J. Eschmeier, K. Laursen and G. Willis, Introduction to Banach Algebras, operators and Harmonic Analysis, Cambridge University Press, Cambridge, 2003.
  8. K. B. Laursen, Algebraci spectral subspaces and automatic continuity, Czechoslovak Math. J., 38 (1988), 157-172. https://doi.org/10.21136/CMJ.1988.102208
  9. K. B. Laursen and M.M. Neumann, An Introduction to Local Spectral Theory, Oxford Science Publications, London Mathematical Society Monographs New Series 20, Oxford, 2000.
  10. T. L. Miller, V. G. Miller and M. M. Neumann, Spectral subspaceas of subsclar operators and related operators, Proc. Amer. Math. Soc., 132 (2003), 1483-1493. https://doi.org/10.1090/S0002-9939-03-07217-4
  11. T. W. Plamer, Banach Algebras and The General Theory of *-algebras Volume I: Algebras and Banach Algebras, Cambridge University Press, Cambridge, 1994.
  12. G. K. Pedersen, Analysis Now, Springer-Verlag, New York, 1988.