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Topological and bornological characterisations of ideals in von Neumann algebras: II

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Abstract

SupposeM is a von Neumann algebra on a Hilbert spaceH andI is any norm closed ideal inM. We extend to this setting the well known fact that the compact operators on a Hilbert space are precisely those whose restrictions to the closed unit ball are weak to norm continuous.

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References

  1. Jurie Conradie. Generalized precompactness and mixed topologies.Collectanae Mathematica, 44:59–70, 1993.

    Google Scholar 

  2. James Bell Cooper.Saks Spaces and Applications to Functional Analysis, volume 28 ofMathematical Studies, North Holland, Amsterdam, 1978.

    Google Scholar 

  3. Klaus Floret.Weakly Compact Sets, volume 801 ofLecute Notes in Mathematics. Springer-Verlag, Berlin, 1980.

    Google Scholar 

  4. D.J.H. Garling. A generalised form of inductive limit topology for vector spaces.Proceedings of the London Mathematical Society, 14:1–28, 1964.

    Google Scholar 

  5. Richard V. Kadison and John R. Ringrose.Fundamentals of the theory of operator algebras. Pure and Applied Mathematics. Academic Press, London, 1983 and 1986.

    Google Scholar 

  6. Victor Kaftal. On the theory of compact operators in von Neumann algebras I.Indiana University Mathematics Journal, 26(3):447–457, 1977.

    Google Scholar 

  7. Victor Kaftal. Relative weak convergence in semifinite von Neumann algebras.Proceedings of the American Mathematical Society, 84(1):89–94, 1982.

    Google Scholar 

  8. Arne Persson, A generalisation of two-norm spaces.Arkiv för Matematik, 5(2):27–36, 1963.

    Google Scholar 

  9. A.P. Robertson and Wendy Robertson.Topological Vector Spaces. Cambridge University Press, 1964.

  10. Anton Ströh.Closed two-sided ideals in a von Neumann algebra and aplications PhD thesis, University of Pretoria, South Africa, 1989.

    Google Scholar 

  11. Graeme West. Ideals of τ-measurable operators. To appear inQuestiones Mathematicae.

  12. Graeme West. Topological and bornological characterisations of ideals in von Neumann algebras: I. To appear inIntegral Equations and Operator Theory.

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Authors and Affiliations

  1. Dept Maths, University of Cape Town, 7700, Rondebosch, South Africa

    Jurie Condradie

  2. Dept Math and Computer Science, Kent State University, 44242, Kent, OH, USA

    Graeme West

Authors
  1. Jurie Condradie
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  2. Graeme West
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Condradie, J., West, G. Topological and bornological characterisations of ideals in von Neumann algebras: II. Integr equ oper theory 23, 49–60 (1995). https://doi.org/10.1007/BF01261202

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  • DOI: https://doi.org/10.1007/BF01261202

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