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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Constructing ultraweakly continuous functionals on $\mathcal B(H)$
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by D. S. Bridges and N. F. Dudley Ward PDF
Proc. Amer. Math. Soc. 126 (1998), 3347-3353 Request permission

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
  • Errett Bishop and Douglas Bridges, Constructive analysis, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 279, Springer-Verlag, Berlin, 1985. MR 804042, DOI 10.1007/978-3-642-61667-9
  • Douglas S. Bridges, On weak operator compactness of the unit ball of $L(H)$, Z. Math. Logik Grundlagen Math. 24 (1978), no. 6, 493–494. MR 511703, DOI 10.1002/malq.19780243104
  • Douglas S. Bridges, A constructive look at positive linear functionals on ${\cal L}(H)$, Pacific J. Math. 95 (1981), no. 1, 11–25. MR 631655, DOI 10.2140/pjm.1981.95.11
  • 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).
  • Douglas Bridges and Fred Richman, A constructive proof of Gleason’s Theorem, to appear.
  • Douglas Bridges, Fred Richman, and Peter Schuster, Polar decompositions, absolute values, and adjoints, to appear.
  • Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition, revue et augmentée. MR 0352996
  • Andrew M. Gleason, Measures on the closed subspaces of a Hilbert space, J. Math. Mech. 6 (1957), 885–893. MR 0096113, DOI 10.1512/iumj.1957.6.56050
  • Hajime Ishihara, Constructive compact operators on a Hilbert space, Ann. Pure Appl. Logic 52 (1991), no. 1-2, 31–37. International Symposium on Mathematical Logic and its Applications (Nagoya, 1988). MR 1104052, DOI 10.1016/0168-0072(91)90037-M
  • Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. I, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR 719020
  • Richard V. Kadison and John R. Ringrose, Fundamentals of the theory of operator algebras. Vol. II, Pure and Applied Mathematics, vol. 100, Academic Press, Inc., Orlando, FL, 1986. Advanced theory. MR 859186, DOI 10.1016/S0079-8169(08)60611-X
  • Gert K. Pedersen, Analysis now, Graduate Texts in Mathematics, vol. 118, Springer-Verlag, New York, 1989. MR 971256, DOI 10.1007/978-1-4612-1007-8
  • Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
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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
  • Received by editor(s): September 1, 1995
  • Received by editor(s) in revised form: April 7, 1997
  • Communicated by: Andreas R. Blass
  • © Copyright 1998 American Mathematical Society
  • 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