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Constructing ultraweakly continuous functionals on $\mathcal{B}(H)$


Authors: D. S. Bridges and N. F. Dudley Ward
Journal: Proc. Amer. Math. Soc. 126 (1998), 3347-3353
MSC (1991): Primary 46S30
DOI: https://doi.org/10.1090/S0002-9939-98-04432-3
MathSciNet review: 1459111
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we give a constructive characterisation of ultraweakly continuous linear functionals on the space of bounded linear operators on a separable Hilbert space.


References [Enhancements On Off] (What's this?)

  • 1. Errett Bishop and Douglas Bridges, Constructive Analysis, Grundlehren der math. Wissenschaften, Bd. 279, Springer-Verlag, Berlin, 1985. MR 87d:03172
  • 2. Douglas Bridges, On weak operator compactness of the unit ball of $L\left( H\right) ,$ Zeit. math. Logik und Grundlagen der Math., 24, 493-494 (1978). MR 80d:03060
  • 3. Douglas Bridges, A constructive look at positive linear functionals on $L$$(H)$, Pacific J. Math. 95(1), 11-25 (1981). MR 84f:47056
  • 4. Douglas Bridges and Hajime Ishihara, Spectra of selfadjoint operators in constructive analysis, Proc. Koninklijke Nederlandse Akad. Wetenschappen, Series A (Indag. Math.), Vol. 7(1), 11-36 (1996).
  • 5. Douglas Bridges and Fred Richman, A constructive proof of Gleason's Theorem, to appear.
  • 6. Douglas Bridges, Fred Richman, and Peter Schuster, Polar decompositions, absolute values, and adjoints, to appear.
  • 7. J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier Villars, Paris, 1969. MR 50:5482
  • 8. Andrew M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6, 885-893 (1957). MR 20:2609
  • 9. Hajime Ishihara, Constructive compact operators on a Hilbert space, Annals of Pure and Applied Logic 52 (1991), 31-37. MR 92c:03066
  • 10. R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras (Vol I), Pure and Applied Mathematics, 100-I, Academic Press, New York, 1983. MR 85j:46099
  • 11. R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras (Vol II), Pure and Applied Mathematics, 100-II, Academic Press, New York, 1986. MR 88d:46106
  • 12. Gert K. Pedersen, Analysis Now, Graduate Texts in Mathematics 118, Springer-Verlag, Berlin, 1989. MR 90f:46001
  • 13. S. Sakai, $C^{*}$-algebras and $W^{*}$-algebras, Ergebnisse der Math. und Ihrer Grenzgebiete, Bd. 60, Springer-Verlag, Berlin, 1971. MR 56:1082

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Additional Information

D. S. Bridges
Affiliation: Department of Mathematics, University of Waikato, Hamilton, New Zealand
Email: douglas@waikato.ac.nz

N. F. Dudley Ward
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, England

DOI: https://doi.org/10.1090/S0002-9939-98-04432-3
Received by editor(s): September 1, 1995
Received by editor(s) in revised form: April 7, 1997
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1998 American Mathematical Society

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