Integral Equations and Operator Theory

, Volume 10, Issue 5, pp 707–720 | Cite as

Elementary operators with H-symbols

  • Raúl E. Curto
  • Lawrence A. Fialkow


Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u1,...,un) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Curto, R.E., The spectra of elementary operators, Indina Univ. Math. J. 32(1983), 193–197.Google Scholar
  2. 2.
    Curto, R.E., Connections between Harte and Taylor spectra, Revue Roum. Math. Pures Appl. 31(1986), 203–215.Google Scholar
  3. 3.
    Curto, R.E., Applications of several complex variables to multiparameter spectral theory, to appear in Lecture Notes in Math., Pitman Publishing Co.Google Scholar
  4. 4.
    Douglas, R.G., Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.Google Scholar
  5. 5.
    Fialkow, L.A., Spectral properties of elementary operators, Acta Sci. Math. 46(1983), 269–282.Google Scholar
  6. 6.
    Fialkow, L.A., Spectral properties of elementary operators II, Trans. Amer. Math. Soc. 290(1985), 415–429.Google Scholar
  7. 7.
    Fialkow, L. A., The index of an elementary operator, Indiana Univ. Math. J. 35(1986), 73–102.Google Scholar
  8. 8.
    Foiaş C. and Mlak, W., The extended spectrum of competely nonunitary contractions and the spectral mapping theorem, Studia Math. 26(1966), 239–245.Google Scholar
  9. 9.
    Harte, R.E., Spectral mapping theorems, Proc. Royal Irish Acad. 72A(1972), 89–107.Google Scholar
  10. 10.
    Harte, R.E., Tensor products, multiplication operators and the spectral mapping theorem, Proc. Royal Irish Acad. 73A(1973), 285–302.Google Scholar
  11. 11.
    Pearcy, C.M., Some recent developments in operator theory, CBMS Regional Conference Series in Mathematics, no. 36, Amer. Math. Soc., Providence, Rhode Island, 1978.Google Scholar
  12. 12.
    Putinar, M., Functional calculus and the Gelfand transformations, Studia Math. 79(1984), 83–86.Google Scholar
  13. 13.
    Rudol, K., On spectral mapping theorems, J. Math. anal. and appl. 97(1983), 131–139.Google Scholar
  14. 14.
    Rudol, K., Extended spectrum of subnormal representations, Bull. Polish Acad. Sci. Math. 31(1983), 361–368.Google Scholar
  15. 15.
    Rudol, K., Spectral mapping theorems for analytic functional calculi, Operator Theory: Adv. and Appl. 17(1986) 331–340.Google Scholar
  16. 16.
    Taylor, J.L., A joint spectrum for several commuting operators, J. Funct. Anal. 6(170, 172–191.Google Scholar
  17. 17.
    Taylor, J. L., The analytic functional calculus for several commuting operators, Acta Math. 125(1970), 1–38.Google Scholar
  18. 18.
    Zelazko, W., An axiomatic approach to joint spectra, I, Studia Math. 64(1979), 250–261.Google Scholar
  19. 19.
    Conway, J.B., Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman Publ., London, 1981.Google Scholar

Copyright information

© Birkhäuser Verlag 1987

Authors and Affiliations

  • Raúl E. Curto
    • 1
  • Lawrence A. Fialkow
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Department of Mathematics and Computer ScienceS.U.N.Y at New PaltzNew PaltzUSA

Personalised recommendations