Abstract
The embedding of a linear set of bounded operators on a separable Hilbert space as a dense subset of the dual of its predual is explored constructively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Michael J. Beeson, Foundations of Constructive Mathematics, Springer—Verlag, Heidelberg, 1985.
Errett Bishop, Foundations of Constructive Analysis, McGraw—Hill, New York, 1967.
Errett Bishop and Douglas Bridges, Constructive Analysis, Grundlehren der math. Wissenschaften 279, Springer—Verlag, Heidelberg, 1985.
Douglas Bridges, “A constructive look at positive linear functionals on L(H) ”,Pacific J. Math. 95(1), 11–25, 1981.
Douglas Bridges, “A constructive look at the real number line”, in Synthèse: Real Numbers, Generalizations of the Reals and Theories of Continua (P. Ehrlich, ed.), pp. 29–92, Kluwer Academic Publishers, Amsterdam, 1994.
Douglas Bridges and Luminita Dediu, “Weak—operator continuity and the existence of adjoints”, Math. Logic Quart. 45, 203–206, 1999.
Douglas Bridges and Luminila Dediu, “Constructing extensions of ultraweakly continuous linear functionals”, J. Functional Analysis, in press.
D.S. Bridges and N.F. Dudley Ward, “Constructing ultraweakly continuous functionals on 8(H)”, Proc. Amer. Math. Soc. 126 (11), 3347–3353, 1998.
Douglas Bridges and Fred Richman, Varieties of Constructive Mathematics,London Math. Soc. Lecture Notes 97 Cambridge University Press, 1987.
Luminila Dediu and Douglas Bridges, “Constructive notes on uniform and locally convex spaces” in Proceedings of 12th International Symposium, FCT ‘89 Iasi, Romania, Springer Lecture Notes in Computer Science 1684, 195–203, 1999.
A. Heyting, “Die formalen Regeln der intuitionistischen Logik”, Sitzungsber. Preuß. Akad. Wiss. Berlin, 42–56, 1930.
R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras (Vol. I ), Academic Press, New York, 1983.
Ker-i Ko, Complexity Theory of Real Functions, Birkhaüser, Boston, 1991.
John Myhill, “Some properties of intuitionistic Zermelo-Fraenkel set theory”, in: Cambridge Summer School in Mathematical Logic(A. Mathias, H. Rogers, eds.), Lecture Notes in Mathematics 337, Springer-Verlag, Berlin, 1973, pp. 206–231.
A.S. Troelstra and D. van Dalen, Constructivism in Mathematics: An Introduction (two volumes), North Holland, Amsterdam, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Dediu, L.V. (2001). Embedding a Linear Subset of B(H) in the Dual of Its Predual. In: Schuster, P., Berger, U., Osswald, H. (eds) Reuniting the Antipodes — Constructive and Nonstandard Views of the Continuum. Synthese Library, vol 306. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9757-9_5
Download citation
DOI: https://doi.org/10.1007/978-94-015-9757-9_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5885-0
Online ISBN: 978-94-015-9757-9
eBook Packages: Springer Book Archive