Mathematische Annalen

, Volume 192, Issue 1, pp 17–32 | Cite as

Spectral mapping theorems for essential spectra

  • Bernhard Gramsch
  • David Lay


Spectral Mapping Essential Spectrum Spectral Mapping Theorem 
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  1. 1.
    Balslev, E., Gamelin, T. W.: The essential spectrum of a class of ordinary differential operators. Pacific J. Math.14, 755–776 (1964).Google Scholar
  2. 2.
    Berger, R.: Fredholmoperatoren in lokalp-konvexen Räumen. Diplomarbeit Mainz 1969.Google Scholar
  3. 3.
    Browder, F. E.: On the spectral theory of elliptic differential operators. I. Math. Ann.142, 22–130 (1961).Google Scholar
  4. 4.
    Dunford, N., Schwartz, J. T.: Linear Operators, Part II. New York: Interscience Publishers 1963.Google Scholar
  5. 5.
    Goldberg, S.: Unbounded linear operators: theory and applications. New York: McGraw-Hill 1966.Google Scholar
  6. 6.
    Gramsch, B.: Spektraleigenschaften analytischer Operatorfunktionen. Math. Z.101, 165–181 (1967).Google Scholar
  7. 7.
    —— Funktionalkalkül mehrerer Veränderlichen in lokalbeschränkten Algebren. Math. Ann.174, 311–344 (1967).Google Scholar
  8. 8.
    -- Über analytische Störungen und den Index von Fredholmoperatoren auf Banachräumen. Dept. Math., Univ. of Maryland TR 69/105, 1–55 (1969).Google Scholar
  9. 9.
    —— Meromorphie in der Theorie der Fredholmoperatoren mit Anwendungen auf elliptische Differentialoperatoren. Math. Ann.188, 97–112 (1970).Google Scholar
  10. 10.
    Gustafson, K., Weidmann, J.: On the essential spectrum. J. Math. Anal. Appl.25, 121–127 (1969).Google Scholar
  11. 11.
    Halmos, P. R.: Introduction to Hilbert space and the theory of spectral multiplicity. Second ed. New York, Chelsea Pub. Co. 1957.Google Scholar
  12. 12.
    Kato, T.: Perturbation theory for nullity, deficiency, and other quantities of linear operators. J. d'Analyse Math.11, 261–322 (1958).Google Scholar
  13. 13.
    Lay, D.: Characterizations of the essential spectrum of F. E. Browder. Bull. A.M.S.74, 246–248 (1968).Google Scholar
  14. 14.
    —— Spectral analysis using ascent, descent, nullity and defect. Math. Ann.184, 197–214 (1970).Google Scholar
  15. 15.
    Pietsch, A.: Zur Theorie der σ-Transformationen in lokalkonvexen Vektorräumen. Math. Nachr.21, 347–369 (1960).Google Scholar
  16. 16.
    Rickart, C. E.: Banach algebras. New York: Van Nostrand 1960.Google Scholar
  17. 17.
    Schechter, M.: On the essential spectrum of an arbitrary operator. J. Math. Anal. Appl.13, 205–215 (1966).Google Scholar
  18. 18.
    Taylor, A. E.: Introduction to functional analysis. New York: Wiley and Sons 1958.Google Scholar
  19. 19.
    —— Theorems on ascent, descent, nullity and defect of linear operators. Math. Ann.163, 18–49 (1966).Google Scholar
  20. 20.
    Wolf, F.: On the essential spectrum of partial differential boundary problems. Comm. Pure Appl. Math.12, 211–228 (1959).Google Scholar
  21. 21.
    Yood, B.: Properties of linear transformations preserved under addition of a completely continuous transformation. Duke Math. J.18, 599–612 (1951).Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • Bernhard Gramsch
    • 1
  • David Lay
    • 2
  1. 1.Fachbereich MathematikUniversität Trier-KaiserslauternKaiserslauternGermany
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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