Integral Equations and Operator Theory

, Volume 72, Issue 3, pp 403–418 | Cite as

The Taylor–Browder Spectrum on Prime C*-Algebras

  • Derek Kitson


We provide a formula for the Taylor–Browder spectrum of a pair (L a , R b ) of left and right multiplication operators acting on a prime C*-algebra with non-zero socle. We also compute ascent and descent for multiplication operators on a prime ring, characterise Browder elements in a prime C*-algebra and discuss upper semicontinuity for the Browder spectrum.

Mathematics Subject Classification (2010)

Primary 47A13 Secondary 47B48 46L05 47A55 18G35 


Browder spectrum Taylor spectrum Browder elements multiplication operators ascent and descent prime C*-algebra 


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  1. 1.
    Ara P., Mathieu M.: Local multipliers of C*-algebras. Springer, London (2003)MATHCrossRefGoogle Scholar
  2. 2.
    Barnes, B.A., Murphy, G., Smith, M.R.F., West, T.T.: Riesz and Fredholm theory in Banach algebras. Research Notes in Mathematics, 67. Pitman (Advanced Publishing Program), Boston (1982)Google Scholar
  3. 3.
    Browder E.: On the spectral theory of elliptic differential operators. I. Math. Ann. 142, 22–130 (1961)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Buoni J.J.: The variation of Browder’s essential spectrum. Proc. Am. Math. Soc. 48, 140–144 (1975)MathSciNetMATHGoogle Scholar
  5. 5.
    Caradus S.R.: Generalized inverses and operator theory. Queen’s Papers in Pure and Applied Mathematics, 50. Queen’s University, Kingston (1978)Google Scholar
  6. 6.
    Curto, R.E.: Spectral theory of elementary operators. In: Mathieu, M. (ed.) Elementary operators and applications (Blaubeuren 1991). World Science Publications, River Edge (1992)Google Scholar
  7. 7.
    Curto R.E., Dash A.T.: Browder spectral systems. Proc. Am. Math. Soc. 103, 407–413 (1988)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Curto R.E., Hernández G.C.: A joint spectral characterisation of primeness for C*-algebras. Proc. Am. Math. Soc. 125, 3299–3301 (1997)MATHCrossRefGoogle Scholar
  9. 9.
    Gramsch B., Lay D.: Spectral mapping theorems for essential spectra. Math. Ann. 192, 17–32 (1971)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Harte R.E., Kitson D.: On Browder tuples. Acta Sci. Math. (Szeged) 75(3–4), 665–677 (2009)MathSciNetGoogle Scholar
  11. 11.
    Kitson D.: Ascent and descent for sets of operators. Studia Math. 191(2), 151–161 (2009)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Lay D.C.: Characterizations of the essential spectrum of F.E. Browder. Bull. Am. Math. Soc. 74, 246–248 (1968)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Mathieu M.: Spectral theory for multiplication operators on C*-algebras. Proc. Roy. Irish Acad. Sect. A 83(2), 231–249 (1983)MathSciNetMATHGoogle Scholar
  14. 14.
    Mathieu M.: Elementary operators on prime C*-algebras. I. Math. Ann. 284, 223–244 (1989)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Newburgh J.D.: The variation of spectra. Duke Math. J. 18, 165–176 (1951)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Taylor J.L.: A joint spectrum for several commuting operators. J. Funct. Anal. 6, 172–191 (1970)MATHCrossRefGoogle Scholar
  17. 17.
    Vala, K.: On compact sets of compact operators. Ann. Acad. Sci. Fenn. Ser. A I 351 1964Google Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.School of MathematicsTrinity CollegeDublin 2Ireland

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