Rocky Mountain Journal of Mathematics

Different Exponential Spectra in Banach Algebras

L. Lindeboom (Groenewald) and H. Raubenheimer

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Rocky Mountain J. Math., Volume 29, Number 3 (1999), 957-970.

First available in Project Euclid: 5 June 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46H05: General theory of topological algebras
Secondary: 46H10: Ideals and subalgebras


Lindeboom (Groenewald), L.; Raubenheimer, H. Different Exponential Spectra in Banach Algebras. Rocky Mountain J. Math. 29 (1999), no. 3, 957--970. doi:10.1216/rmjm/1181071617.

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  • W. Arendt, On the o-spectrum of regular operators and the spectrum of measures, Math. Z. 178 (1981), 271-287.
  • B. Aupetit, A primer on spectral theory, Springer-Verlag, Berlin, New York, 1991.
  • B.A. Barnes, G.J. Murphy, M.R.F. Smyth and T.T. West, Riesz and Fredholm theory in Banach algebras, Res. Notes Math. 67, Advanced Publishing Program, Pitman, Boston-London-Melbourne, 1982.
  • F.F. Bosnall and J. Duncan, Complete normed algebras, Springer Verlag, New York, 1973.
  • L. Burlando, Comparisons between different spectra of an element in a Banach algebra, Internat. J. Math. Math. Sci. 16 (1993), 819-822.
  • J.B. Conway, Functions of one complex variable, Springer-Verlag, New York, 1978.
  • J.J. Grobler and H. Raubenheimer, Spectral properties of an element in different Banach algebras, Glasgow Math. J. 33 (1991), 11-20.
  • L. Groenewald, A note on different exponential spectra of an element in a Banach algebra, Quaestiones Math. 15 (1992), 39-45.
  • L. Groenewald, R.E. Harte and H. Raubenheimer, Perturbation by inessential and Riesz elements, Quaestiones Math. 12 (1989), 439-446.
  • L. Groenewald and H. Raubenheimer, A note on the singular and exponential spectrum in Banach algebras, Quaestiones Math. 11 (1988), 399-408.
  • R.E. Harte, The exponential spectrum in Banach algebras, Proc. Amer. Math. Soc. 58 (1976), 114-118.
  • --------, On rank one elements, Studia Math. 117 (1995), 73-77.
  • R.E. Harte and H. Raubenheimer, Fredholm. Weyl and Browder theory III, Proc. Roy. Irish. Acad. Sect. A 95 (1995), 11-16.
  • A. Lebow and M. Schechter, Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7 (1971), 1-26.
  • H. du T. Mouton, On inessential ideals in Banach algebras, Quaestiones Math. 17 (1994), 59-66.
  • H. du T. Mouton and H. Raubenheimer, Fredholm theory relative to two Banach algebra homomorphisms, Quaestiones Math. 14 (1991), 371-382.
  • --------, More on Fredholm theory relative to a Banach algebra homomorphism, Proc. Roy. Irish Acad. Sect. A 93 (1993), 17-25.
  • G.J. Murphy, The index group, the exponential spectrum, and some spectral containment theorems, Proc. Roy. Irish Acad. Sect. A 92 (1992), 229-238.
  • J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28 (1978), 656-676.
  • W. Rudin, Functional analysis, McGraw-Hill, Inc., New York, 1973.