Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A Note on the Spectral Mapping Theorem

  • Jung, Il Bong (Department of Mathematics, Kyungpook National University) ;
  • Ko, Eungil (Department of Mathematics, Ewha Women's University) ;
  • Pearcy, Carl (Department of Mathematics, Texas A&M University)
  • Received : 2005.11.18
  • Published : 2007.03.23
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Abstract

In this note we point out how a theorem of Gamelin and Garnett from function theory can be used to establish a spectral mapping theorem for an arbitrary contraction and an associated class of $H^{\infty}$-functions.

Keywords

References

  1. H. Bercovici, C. Foias and C. Pearcy, A spectral mapping theorem for functions with nite Dirichlet integral, J. Reine Angew Math., 366(1986), 1-17.
  2. H. Bercovici, C. Foias and C. Pearcy, Dual algebras with applications to invariant subspaces and dilation theory, CBMS regional Conference Series, No.56, Amer. Math. Soc., Providence, R. I. 1985.
  3. A. Brown and C. Pearcy, Introduction to Operator Theory I: Elements of Functional Analysis, Springer-Verlag, New York, 1977.
  4. J. Conway and B. Morrel, Operators that are points of spectral continuity, Integral Equations Operator Theory, 2 (1979), 175-198.
  5. C. Foias and W. Mlak, The extended spectrum of completely non-unitary contractions and the spectral mapping theorem, Studia Math., 26(1966), 239-245. https://doi.org/10.4064/sm-26-3-239-245
  6. C. Foias, B. Sz.-Nagy, and C. Pearcy, Functional models and extended spectral dominance, Acta Sci. Math., 43(1981), 243-254.
  7. C. Foias and C. Pearcy, (BCP)-operators and enrichment of invariant subspace lattices, J. Operator Theory, 9(1983), 187-202.
  8. C. Foias and J. Williams, Some remarks on the Voltera operator, Proc. Amer. Math. Soc., 31(1972), 177-184. https://doi.org/10.1090/S0002-9939-1972-0295126-2
  9. T. Gamelin and J. Garnett, Uniform approximation to bounded analytic functions, Revista de la Union Mathematica Argentina, 25(1970), 87-94.
  10. J. Newburgh, The variation of spectra, Duke Math. J., 18(1951), 165-176. https://doi.org/10.1215/S0012-7094-51-01813-3
  11. B. Sz-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970.