Square Roots and Powers in Constructive Banach Algebra Theory

  • Douglas S. Bridges
  • Robin S. Havea
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

Several new and improved results about positive integral powers of hermitian elements, and square roots of positive elements, in a Banach algebra are proved constructively.

Keywords

State Space Convex Hull Extreme Point Banach Algebra Positive Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Berger, J., Schuster, P.M.: Dini’s theorem in the light of reverse mathematics. In: Lindström, S., Palmgren, E., Segerberg, K., Stoltenberg-Hansen, V. (eds.) Logicism, Intuitionism, and Formalism—What has become of them? Synthèse Library, vol. 341, pp. 153–166. Springer, Dordrecht (2009)Google Scholar
  2. 2.
    Bishop, E.A., Bridges, D.S.: Constructive Analysis. Grundlehren der Mathematischen Wissenschaften, vol. 279. Springer, Berlin (1985)MATHCrossRefGoogle Scholar
  3. 3.
    Bonsall, F.F., Duncan, J.: Complete Normed Algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 80. Springer, Berlin (1973)MATHGoogle Scholar
  4. 4.
    Bridges, D.S., Havea, R.S.: Approximating the numerical range in a Banach algebra. In: Crosilla, L., Schuster, P. (eds.) From Sets and Types to Topology and Analysis. Oxford Logic Guides, pp. 293–303. Clarendon Press, Oxford (2005)CrossRefGoogle Scholar
  5. 5.
    Bridges, D.S., Havea, R.S.: Constructing square roots in a Banach algebra. Sci. Math. Japon. 70(3), 355–366 (2009)MathSciNetMATHGoogle Scholar
  6. 6.
    Bridges, D.S., Havea, R.S.: Powers of a Hermitian element. New Zealand J. Math. 36, 1–10 (2007)MathSciNetMATHGoogle Scholar
  7. 7.
    Bridges, D.S., Richman, F.: Varieties of Constructive Mathematics. London Math. Soc. Lecture Notes, vol. 97. Cambridge Univ. Press (1987)Google Scholar
  8. 8.
    Bridges, D.S., Vîţă, L.S.: Techniques of Constructive Analysis. Universitext. Springer, New York (2006)MATHCrossRefGoogle Scholar
  9. 9.
    Havea, R.S.: On Firmness of the State Space and Positive Elements of a Banach Algebra. J. UCS 11(12), 1963–1969 (2005)MathSciNetMATHGoogle Scholar
  10. 10.
    Holmes, R.B.: Geometric Functional Analysis and its Applications. Graduate Texts in Mathematics, vol. 24. Springer, New York (1975)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Douglas S. Bridges
    • 1
  • Robin S. Havea
    • 2
  1. 1.Department of Mathematics & StatisticsUniversity of CanterburyChristchurchNew Zealand
  2. 2.Department of Mathematics & Computing ScienceUniversity of the South PacificSuvaFiji

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