충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제36권1호
  • /
  • Pages.13-23
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  • 2023
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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GENERALIZED INTERTWINING LINEAR OPERATORS WITH ISOMETRIES

  • Hyuk Han (Division of Liberal Arts Kongju National University)
  • 투고 : 2023.01.11
  • 심사 : 2023.01.29
  • 발행 : 2023.02.28
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초록

In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

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참고문헌

  1. P. Aiena, Fredholm 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, Gewerbestrasse, 2018. 
  3. E. Albrecht and J. Eschmeier, Analytic functional models and local spectral theory, Proc. London Math. Soc., 75 (1997), no. 3, 323-348.  https://doi.org/10.1112/S0024611597000373
  4. I. Colojoara and C. Foias, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968. 
  5. H. G. Dales, Automatic continuity: A survey, Bull. London Math. Soc. 10 (1978), no. 2, 129-183.  https://doi.org/10.1112/blms/10.2.129
  6. H. G. Dales, Radical Banach Algebras and Automatic Continuity, Clarendon Press, Oxford, 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 Automatic continuity of intertwiners in topological vector spaces, Progress in Functional Analysis, North-Holland Mathematics Studies 170, North-Holland, Amsterdam, 179-190, 1992. 
  9. K. B. Laursen and M. M. Neumann, Automatic continuity of intertwining linear operators on Banach spaces, Rendiconti del Circolo Mathematico di Palermo Series 2, 40 (1991), 325-341.  https://doi.org/10.1007/BF02845071
  10. K. B. Laursen and M.M. Neumann, An Introduction to Local Spectral Theory, Oxford University Press, Oxford, 2000. 
  11. M. M. Neumann, Decomposable operators and generalized intertwining linear transformations, Special Class of Linear Operators and Other Topics, Operator Theory: Advances and Applications Vol. 28, Birkhauser Verlag, Basel, 209-222, 1988. 
  12. A. M. Sinclair, Automatic Continuity of Linear Operators, Cambridge University Press, Cambridge, 1976.